Download Differential Geometry of Curves and Surfaces by Kristopher Tapp (auth.) PDF

By Kristopher Tapp (auth.)

This is a textbook on differential geometry well-suited to numerous classes in this subject. For readers looking an hassle-free textual content, the necessities are minimum and contain lots of examples and intermediate steps inside proofs, whereas supplying a call for participation to extra excursive functions and complicated themes. For readers certain for graduate tuition in math or physics, this can be a transparent, concise, rigorous improvement of the subject together with the deep international theorems. For the good thing about all readers, the writer employs a variety of innovations to render the tough summary rules herein extra comprehensible and engaging.
Over three hundred colour illustrations carry the math to existence, immediately clarifying techniques in ways in which grayscale couldn't. Green-boxed definitions and purple-boxed theorems aid to visually set up the mathematical content material. colour is even used in the textual content to spotlight logical relationships.
Applications abound! The examine of conformal and equiareal features is grounded in its program to cartography. Evolutes, involutes and cycloids are brought via Christiaan Huygens' interesting tale: in trying to clear up the recognized longitude challenge with a mathematically-improved pendulum clock, he invented arithmetic that may later be utilized to optics and gears. Clairaut’s Theorem is gifted as a conservation legislations for angular momentum. Green’s Theorem makes attainable a drafting software referred to as a planimeter. Foucault’s Pendulum is helping one visualize a parallel vector box alongside a range of the earth. Even higher, a south-pointing chariot is helping one visualize a parallel vector box alongside any curve in any surface.
In fact, the main profound program of differential geometry is to trendy physics, that is past the scope of this ebook. The GPS in any vehicle wouldn’t paintings with out normal relativity, formalized during the language of differential geometry. all through this e-book, functions, metaphors and visualizations are instruments that inspire and make clear the rigorous mathematical content material, yet by no means change it.

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Download Differentialgeometrie und Minimalflächen by Jost-Hinrich Eschenburg, Jürgen Jost PDF

By Jost-Hinrich Eschenburg, Jürgen Jost

Das vorliegende Lehrbuch bietet eine moderne Einführung in die Differenzialgeometrie - etwa im Umfang einer einsemestrigen Vorlesung. Zunächst behandelt es die Geometrie von Flächen im Raum. Viele Beispiele schulen Leser in geometrischer Anschauung, deren wichtigste Klasse die Minimalflächen bilden. Zu ihrem Studium entwickeln die Autoren analytische Methoden und lösen in diesem Zusammenhang das Plateausche challenge. Es besteht darin, eine Minimalfläche mit vorgegebener Berandung zu finden. Als Beispiel einer globalen Aussage der Differenzialgeometrie beweisen sie den Bernsteinschen Satz. Weitere Kapitel behandeln die innere Geometrie von Flächen einschließlich des Satzes von Gauss-Bonnet, und stellen die hyperbolische Geometrie ausführlich dar. Die Autoren verknüpfen geometrische Konstruktionen und analytische Methoden und folgen damit einem zentralen development der modernen mathematischen Forschung. Verschiedene geistesgeschichtliche Bemerkungen runden den textual content ab. Die Neuauflage wurde überarbeitet und aktualisiert.

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Download Morse Theory and Floer Homology by Michèle Audin PDF

By Michèle Audin

This e-book is an advent to fashionable tools of symplectic topology. it really is dedicated to explaining the answer of a massive challenge originating from classical mechanics: the 'Arnold conjecture', which asserts that the variety of 1-periodic trajectories of a non-degenerate Hamiltonian procedure is bounded lower than by means of the size of the homology of the underlying manifold.

The first half is an intensive advent to Morse idea, a basic software of differential topology. It defines the Morse complicated and the Morse homology, and develops a few of their applications.

Morse homology additionally serves an easy version for Floer homology, that is coated within the moment half. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been the most important within the fresh achievements in symplectic geometry and particularly within the evidence of the Arnold conjecture. The development blocks of Floer homology are extra tricky and indicate using extra subtle analytical equipment, all of that are defined during this moment part.

The 3 appendices current a couple of necessities in differential geometry, algebraic topology and analysis.

The e-book originated in a graduate path given at Strasbourg college, and incorporates a huge variety of figures and workouts. Morse thought and Floer Homology should be relatively worthwhile for graduate and postgraduate students.

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Download Manifolds of Nonpositive Curvature by Werner Ballmann PDF

By Werner Ballmann

This quantity provides a whole and self-contained description of recent leads to the speculation of manifolds of nonpositive curvature. it's in response to lectures added through M. Gromov on the Collège de France in Paris. between others those lectures possibility neighborhood and international pressure difficulties (e.g., a generalization of the recognized Mostow tension theorem) and finiteness effects for manifolds of finite quantity. V. Schroeder wrote up those lectures, together with whole and designated proofs. loads of historical past fabric is additional to the 1st lectures. for that reason this booklet can also function an creation to the topic of nonpositively curved manifolds. the most recent growth during this zone is mirrored within the article of W. Ballmann describing the constitution of manifolds of upper rank.

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Download Riemannian geometry and geometric analysis by Jürgen Jost PDF

By Jürgen Jost

This validated reference paintings keeps to guide its readers to a couple of the most well liked subject matters of latest mathematical research.This new version introduces and explains the tips of the parabolic tools that experience lately came across the sort of staggering luck within the paintings of Perelman on the examples of closed geodesics and harmonic types. It additionally discusses additional examples of geometric variational difficulties from quantum box thought, one other resource of profound new rules and techniques in geometry.

From the reviews

"This publication offers a truly readable advent to Riemannian geometry and geometric research. the writer makes a speciality of utilizing analytic tools within the learn of a few basic theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparability theorem, the Lyusternik and Fet theorem and the life of harmonic mappings. With the massive improvement of the mathematical topic of geometric research, the current textbook is so much welcome. [..] The ebook is made extra fascinating by means of the views in a number of sections." Mathematical Reviews

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Download Principal Bundles: The Classical Case (Universitext) by Stephen Bruce Sontz PDF

By Stephen Bruce Sontz

This introductory graduate point textual content presents a comparatively fast route to a different subject in classical differential geometry: significant bundles. whereas the subject of central bundles in differential geometry has develop into vintage, even usual, fabric within the smooth graduate arithmetic curriculum, the original strategy taken during this textual content offers the fabric in a fashion that's intuitive for either scholars of arithmetic and of physics. The target of this ebook is to give very important, glossy geometric rules in a sort easily obtainable to scholars and researchers in either the physics and arithmetic groups, offering each one with an knowing and appreciation of the language and ideas of the opposite.

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Download Géométrie projective by Jean-Claude Sidler PDF

By Jean-Claude Sidler

    Rendre claires et séduisantes les démonstrations des grands classiques de los angeles géométrie airplane sous l’éclairage de los angeles géométrie projective, tel est l’objectif de ce livre.
    Suivant comme fil conducteur les notions d’homographie et de dualité, Jean-Claude Sidler démontre, dans un langage uncomplicated et moderne, des théorèmes d’une grande souplesse et d’une grande fécondité, qui ont pour nom Pappus, Desargues, Pascal, Chasles… Cette approche originale dégage l’essentiel et advisor naturellement vers des strategies rapides et élégantes de l. a. plupart des problèmes de géométrie plane.
    Dans cette deuxième édition entièrement revue et corrigée, un complément sur les isométries et les similitudes à été ajoute ainsi que de nouveaux exercices et problèmes corrigés.

Le présent ouvrage offrira une aide précieuse aux étudiants, aux candidats au CAPES et à l’agrégation — voire aux ingénieurs ayant besoin de s’initier aux méthodes projectives — ainsi qu’aux enseignants souhaitant cultiver ou remettre à l’honneur l’enseignement de l. a. géométrie.

===== desk des matières =====

Préface

Avant-propos

Avertissement au lecteur

Chapitre 1 — Généralités sur les espaces projectifs

    1.1 Espace projectif
    1.2 Coordonnées homogènes
    1.3 Cartes affines
        1.3.1 Carte affine d’une droite projective
        1.3.2 Carte affine d’un plan projectif
        1.3.3 Du bon utilization d’une carte affine
    1.4 Homographies
        1.4.1 Propriétés générales des homographies
        1.4.2 Repère projectif
    1.5 Birapport de quatre issues alignés
        1.5.1 Formules utiles
        1.5.2 Quelques résultats utiles
    1.6 Rapport harmonique de quatre issues alignés
    1.7 Dualité dans le plan projectif
        1.7.1 Corrélations
        1.7.2 Propositions duales
    1.8 Birapport de quatre droites concourantes
    1.9 Complexification du plan projectif réel
    1.10 Compléments sur le plan projectif réel

Chapitre 2 — Homographies entre droites projectives

    2.1 Généralités
    2.2 Les projections
        2.2.1 awl d’homographie
        2.2.2 development de l’axe d’une homographie entre droites projectives
    2.3 Expressions analytiques
    2.4 Faisceaux de droites d’un plan projectif
        2.4.1 Projections
        2.4.2 Centre d’homographie
        2.4.3 Homographies entre droites projectives et faisceaux de droites
    2.5 Exercices

Chapitre three — Groupe des homographies d’une droite projective

    3.1 issues fixes d’une homographie : définitions et généralités
    3.2 Involutions
    3.3 Propriétés des homographies hyperboliques
    3.4 Homographies paraboliques
    3.5 Homographies elliptiques d’une droite projective réelle
    3.6 buildings géométriques
    3.7 Théorème duaux
    3.8 Deuxième théorème de Desargues
    3.9 Exercices

Chapitre four — Homographies du plan projectif

    4.1 Détermination d’une homographie plane
        4.1.1 issues fixes d’une homographie
        4.1.2 category des homographies d’un plan projectif réel
        4.1.3 Droites invariantes d’une homographie plane
    4.2. Les homologies
        4.2.1 building géométrique de l’image d’un element par une homologie
        4.2.2 Les homologies dans une carte affine
    4.3 Les differences affines
    4.4 Les involutions du plan projectif
    4.5 Générateurs du groupe projectif
    4.6 Quelques propriétés classiques
    4.7 Orthogonalité
        4.7.1 Involution canonique
        4.7.2 issues cycliques
    4.8 Similitudes
        4.8.1 perspective de deux droites. Bissectrices
        4.8.2 Déplacements
    4.9 Exercices

Chapitre five — Homographies et coniques

    5.1 Description géométrique d’une conique
        5.1.1 Cas particulier où los angeles conique est dégénérée
        5.1.2 Autres formulations du théorème de Chasles-Steiner
        5.1.3 Tangentes à une conique définie par une homographie
        5.1.4 Birapport de quatre issues d’une conique propre
        5.1.5 issues conjugués harmoniques sur une conique
    5.2 Homographie d’une conique sur elle-même
        5.2.1 Projection d’une conique sur une droite
        5.2.2 Homographies d’une conique et homographies planes
    5.3 Décomposition d’une homographie. awl d’homographie
    5.4 Coniques affines
        5.4.1 Arc capable
        5.4.2 Les rotations
        5.4.3 l. a. géométrie de Lobatchevsky
    5.5 Coniques tangentielles
        5.5.1 Transformation par polaire réciproque
        5.5.2 Homographies et coniques tangentielles
        5.5.3 Tangentes à los angeles conique
        5.5.4 Birapport de quatre tangentes à une conique
        5.5.5 Homographie entre les tangentes à une même conique propre
    5.6 Exercices

Chapitre 6 — Faisceaux de coniques dans un plan projectif complexe

    6.1 Les faisceaux de coniques et leur classification
    6.2 type des faisceaux non dégénérés du plan projectif complexe
    6.3 Faisceaux et polarité
        6.3.1 Conique des onze points
        6.3.2 Coniques affines
        6.3.3 Conique des neuf points
        6.3.4 Le cercle d’Euler
    6.4 Troisième théorème de Desargues
    6.5 Faisceaux tangentiels
        6.5.1 Classification
        6.5.2 Exemples de faisceaux tangentiels
    6.6 Exercices

Chapitre 7 — Exercices de référence

Chapitre eight — Problèmes classiques

    8.1 Triangles et cercles. Problèmes classiques sous l’éclairage projectif
    8.2 Lieux et enveloppes
    8.3 Coniques homologiques
    8.4 Quelques cas particuliers du grand théorème de Poncelet
    8.5 Six ou huit issues sur une conique
    8.6 Quelques propriétés classiques des coniques affines

Solutions des exercices de fin de chapitre

Appendice — Rappel de quelques définitions

    A.1 Espaces projectifs
    A.2 Équation d’une droite
    A.3 Coniques d’un plan projectif

Bibliographie

Index

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Download Geometric Analysis on the Heisenberg Group and Its by Ovidiu Calin PDF

By Ovidiu Calin

The idea of subRiemannian manifolds is heavily on the topic of Hamiltonian mechanics. during this e-book, the authors research the houses and purposes of subRiemannian manifolds that immediately fulfill the Heisenberg precept, that could be important in quantum mechanics. specifically, the habit of geodesics during this atmosphere performs a big function find warmth kernels and propagators for Schr?¶dinger's equation. one of many novelties of this publication is the creation of innovations from advanced Hamiltonian mechanics. Titles during this sequence are co-published with foreign Press, Cambridge, MA.

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Download Algorithmic Topology and Classification of 3-Manifolds by Sergei Matveev PDF

By Sergei Matveev

From the studies of the first variation: "This ebook presents a finished and certain account of other themes in algorithmic three-d topology, culminating with the popularity method for Haken manifolds and together with the updated leads to machine enumeration of 3-manifolds. Originating from lecture notes of varied classes given through the writer over a decade, the booklet is meant to mix the pedagogical process of a graduate textbook (without workouts) with the completeness and reliability of a examine monograph… the entire fabric, with few exceptions, is gifted from the atypical perspective of exact polyhedra and specific spines of 3-manifolds. This selection contributes to maintain the extent of the exposition rather basic. In end, the reviewer subscribes to the citation from the again disguise: "the e-book fills a niche within the present literature and should develop into a typical reference for algorithmic three-dimensional topology either for graduate scholars and researchers". Zentralblatt f?r Mathematik 2004 For this second variation, new effects, new proofs, and commentaries for a greater orientation of the reader were additional. particularly, in bankruptcy 7 a number of new sections pertaining to functions of the pc software "3-Manifold Recognizer" were integrated.

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Download Conformal Symmetry Breaking Operators for Differential Forms by Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner PDF

By Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner

This paintings is the 1st systematic learn of all attainable conformally covariant differential operators remodeling differential kinds on a Riemannian manifold X into these on a submanifold Y with concentrate on the version area (X, Y) = (Sn, Sn-1).

The authors provide an entire type of all such conformally covariant differential operators, and locate their specific formulæ within the flat coordinates by way of uncomplicated operators in differential geometry and classical hypergeometric polynomials. ensuing households of operators are average generalizations of the Rankin–Cohen brackets for modular types and Juhl's operators from conformal holography. The matrix-valued factorization identities between all attainable combos of conformally covariant differential operators also are established.

The major equipment of the facts will depend on the "F-method" lately brought and built by means of the authors. it's a basic approach to build intertwining operators among C-induced representations or to discover singular vectors of Verma modules within the context of branching principles, as options to differential equations at the Fourier rework part. The e-book provides a brand new extension of the F-method to the matrix-valued case within the common surroundings, that may be utilized to different difficulties as well.

This booklet bargains a self-contained creation to the research of symmetry breaking operators for infinite-dimensional representations of reductive Lie teams. this option could be valuable for lively scientists and available to graduate scholars and younger researchers in differential geometry, illustration conception, and theoretical physics.

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