Heat Kernels and Dirac Operators by Nicole Berline PDF

By Nicole Berline

ISBN-10: 3540200622

ISBN-13: 9783540200628

During this ebook, the Atiyah-Singer index theorem for Dirac operators on compact Riemannian manifolds and its newer generalizations obtain basic proofs. the most process that's used is an specific geometric development of the warmth kernels of a generalized Dirac operator. the 1st 4 chapters will be used on the textual content for a graduate path at the functions of linear elliptic operators in differential geometry and the single must haves are a familiarity with easy differential geometry. numerous chapters take care of different preparatory fabric.

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Get Index Theorem. 1 PDF

By Mikio Furuta

ISBN-10: 0821820974

ISBN-13: 9780821820971

The Atiyah-Singer index theorem is a extraordinary outcome that permits one to compute the distance of ideas of a linear elliptic partial differential operator on a manifold when it comes to in basic terms topological facts concerning the manifold and the logo of the operator. First proved by means of Atiyah and Singer in 1963, it marked the start of a very new course of study in arithmetic with family members to differential geometry, partial differential equations, differential topology, K-theory, physics, and different parts. The author's major target during this quantity is to provide a whole facts of the index theorem. The model of the evidence he chooses to provide is the single in keeping with the localization theorem. the must haves comprise a primary path in differential geometry, a few linear algebra, and a few evidence approximately partial differential equations in Euclidean areas.

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Shiing-Shen Chern, Zhongmin Shen's Riemann-Finsler Geometry PDF

By Shiing-Shen Chern, Zhongmin Shen

ISBN-10: 9812383573

ISBN-13: 9789812383570

ISBN-10: 9812383581

ISBN-13: 9789812383587

Riemann-Finsler geometry is a topic that matters manifolds with Finsler metrics, together with Riemannian metrics. It has purposes in lots of fields of the traditional sciences. Curvature is the critical proposal in Riemann–Finsler geometry. This necessary textbook offers special discussions on very important curvatures reminiscent of the Cartan torsion, the S-curvature, the Landsberg curvature and the Riemann curvature. It additionally bargains with Finsler metrics with distinct curvature or geodesic houses, equivalent to projectively flat Finsler metrics, Berwald metrics, Finsler metrics of scalar flag curvature or isotropic S-curvature, and so on. Instructive examples are given in abundance, for extra description of a few vital geometric options. The textual content comprises the latest effects, even supposing the various difficulties mentioned are classical.

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Read e-book online Invariant Probabilities of Markov-Feller Operators and Their PDF

By Radu Zaharopol

ISBN-10: 376437134X

ISBN-13: 9783764371340

This booklet covers invariant chances for a wide classification of discrete-time homogeneous Markov tactics often called Feller procedures. those Feller tactics seem within the learn of iterated functionality platforms with possibilities, convolution operators, and sure time sequence.

From the reviews:

''A very invaluable reference for researchers wishing to go into the realm of desk bound Markov methods either from a probabilistic and a dynamical element of view.'' --MONATSHEFTE FÜR MATHEMATIK

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Gianna Stefani, Ugo Boscain, Jean-Paul Gauthier, Andrey's Geometric Control Theory and Sub-Riemannian Geometry PDF

By Gianna Stefani, Ugo Boscain, Jean-Paul Gauthier, Andrey Sarychev, Mario Sigalotti

ISBN-10: 3319021311

ISBN-13: 9783319021317

ISBN-10: 331902132X

ISBN-13: 9783319021324

Honoring Andrei Agrachev's sixtieth birthday, this quantity offers contemporary advances within the interplay among Geometric keep an eye on thought and sub-Riemannian geometry. at the one hand, Geometric keep watch over concept used the differential geometric and Lie algebraic language for learning controllability, movement making plans, stabilizability and optimality for keep watch over structures. The geometric process became out to be fruitful in functions to robotics, imaginative and prescient modeling, mathematical physics and so forth. however, Riemannian geometry and its generalizations, reminiscent of sub-Riemannian, Finslerian geometry etc., were actively adopting tools constructed within the scope of geometric keep an eye on. software of those equipment has resulted in vital effects relating to geometry of sub-Riemannian areas, regularity of sub-Riemannian distances, homes of the crowd of diffeomorphisms of sub-Riemannian manifolds, neighborhood geometry and equivalence of distributions and sub-Riemannian buildings, regularity of the Hausdorff quantity, etc.

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Geometry of Manifolds with Non-negative Sectional Curvature: - download pdf or read online

By Owen Dearricott

ISBN-10: 3319063723

ISBN-13: 9783319063720

ISBN-10: 3319063731

ISBN-13: 9783319063737

Providing an updated review of the geometry of manifolds with non-negative sectional curvature, this quantity provides a close account of the newest examine within the region. The lectures disguise a variety of issues comparable to basic isometric team activities, circle activities on certainly curved 4 manifolds, cohomogeneity one activities on Alexandrov areas, isometric torus activities on Riemannian manifolds of maximal symmetry rank, n-Sasakian manifolds, isoparametric hypersurfaces in spheres, touch CR and CR submanifolds, Riemannian submersions and the Hopf conjecture with symmetry. additionally integrated is an advent to the speculation of external differential systems.

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Download e-book for kindle: Integral Geometry and Radon Transforms by Sigurdur Helgason

By Sigurdur Helgason

ISBN-10: 1441960546

ISBN-13: 9781441960542

ISBN-10: 1441960554

ISBN-13: 9781441960559

In this article, crucial geometry offers with Radon’s challenge of representing a functionality on a manifold when it comes to its integrals over yes submanifolds—hence the time period the Radon remodel. Examples and far-reaching generalizations bring about primary difficulties equivalent to: (i) injectivity, (ii) inversion formulation, (iii) aid questions, (iv) purposes (e.g., to tomography, partial differential equations and staff representations). For the case of the aircraft, the inversion theorem and the help theorem have had significant functions in drugs via tomography and CAT scanning. whereas containing a few fresh learn, the booklet is aimed toward starting graduate scholars for school room use or self-study. a couple of workouts aspect to additional effects with documentation. From the reports: “Integral Geometry is an engaging quarter, the place a number of branches of arithmetic meet jointly. The contents of the e-book is targeted round the duality and double fibration, that's discovered throughout the masterful remedy of a number of examples. The e-book is written by means of knowledgeable, who has made primary contributions to the area.” —Boris Rubin, Louisiana kingdom University

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New PDF release: Géométrie projective

By Jean-Claude Sidler

ISBN-10: 2100052349

ISBN-13: 9782100052349

    Rendre claires et séduisantes les démonstrations des grands classiques de l. a. géométrie aircraft 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 easy 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 consultant naturellement vers des options rapides et élégantes de los angeles 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 los angeles géométrie.

===== desk des matières =====



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 building 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 structures 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 type des homographies d’un plan projectif réel
        4.1.3 Droites invariantes d’une homographie plane
    4.2. Les homologies
        4.2.1 development géométrique de l’image d’un element par une homologie
        4.2.2 Les homologies dans une carte affine
    4.3 Les adjustments 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 los angeles 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 l. a. 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



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