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Variétés de contact. --- Contact manifolds --- Geometrie differentielle --- Variétés de contact.
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Geometry, Differential --- Symplectic geometry --- Contact manifolds --- Géométrie différentielle --- Géométrie symplectique --- Variétés de contact --- Géométrie différentielle. --- Géométrie symplectique. --- Variétés de contact. --- Géométrie différentielle. --- Géométrie symplectique. --- Variétés de contact.
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Lie, Algèbres de. --- Lie algebras. --- Variétés de contact --- Contact manifolds --- Lie, Algèbres de. --- Variétés de contact
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Vector bundles. --- Invariants --- Fibrés vectoriels. --- Variétés de contact. --- Contact manifolds --- Geometrie differentielle --- Formes differentielles --- Fibrés vectoriels. --- Variétés de contact.
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Group theory --- Geometry, Differential. --- Contact manifolds --- Group theory. --- Géométrie différentielle --- Variétés de contact (Géométrie) --- Groupes, Théorie des --- Contact manifolds. --- Mathematics--series --- Théorie des groupes --- Géométrie différentielle. --- Variétés de contact. --- Géométrie différentielle --- Variétés de contact (Géométrie) --- Théorie des groupes
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Geometry, Differential --- Symplectic manifolds --- Hamiltonian systems --- Congresses --- Symplectic geometry --- Contact manifolds --- Géométrie différentielle --- Géométrie symplectique --- Variétés de contact --- Géométrie différentielle. --- Géométrie symplectique. --- Variétés de contact. --- Geometry, Differential - Congresses --- Symplectic manifolds - Congresses --- Hamiltonian systems - Congresses --- Géométrie différentielle. --- Géométrie symplectique. --- Variétés de contact.
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This second edition, divided into fourteen chapters, presents a comprehensive treatment of contact and symplectic manifolds from the Riemannian point of view. The monograph examines the basic ideas in detail and provides many illustrative examples for the reader. Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition provides new material in most chapters, but a particular emphasis remains on contact manifolds. New principal topics include a complex geodesic flow and the accompanying geometry of the projectivized holomorphic tangent bundle and a complex version of the special directions discussed in Chapter 11 for the real case. Both of these topics make use of Étienne Ghys's attractive notion of a holomorphic Anosov flow. Researchers, mathematicians, and graduate students in contact and symplectic manifold theory and in Riemannian geometry will benefit from this work. A basic course in Riemannian geometry is a prerequisite. Reviews from the First Edition: "The book . . . can be used either as an introduction to the subject or as a reference for students and researchers . . . [it] gives a clear and complete account of the main ideas . . . and studies a vast amount of related subjects such as integral sub-manifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics." Mathematical Reviews " ¦this is a pleasant and useful book and all geometers will profit [from] reading it. They can use it for advanced courses, for thesis topics as well as for references. Beginners will find in it an attractive [table of] contents and useful ideas for pursuing their studies." Memoriile Sectiilor Stiintifice
Contact manifolds --- Symplectic manifolds --- Geometry, Riemannian --- Variétés de contact (Géométrie) --- Variétés symplectiques --- Riemann, Géométrie de --- Variétés de contact (Géométrie) --- Variétés symplectiques --- Riemann, Géométrie de --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B
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Differential geometry. Global analysis --- Symplectic geometry --- Mechanics, Analytic --- Géométrie symplectique --- Mécanique analytique --- 514.75 --- Differential geometry in spaces with fundamental groups --- Mechanics, Analytic. --- Symplectic geometry. --- 514.75 Differential geometry in spaces with fundamental groups --- Géométrie symplectique --- Mécanique analytique --- Symplectic manifolds --- Variétés symplectiques --- Poisson, Variétés de --- Poisson manifolds --- Manifolds (Mathematics) --- Variétés (mathématiques) --- Variétés de contact --- Contact manifolds --- Géometrie différentielle
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Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology).
Contact manifolds --- Differential equations, Nonlinear --- Variétés de contact (Géométrie) --- Equations différentielles non linéaires --- Contact manifolds. --- Differential equations, Nonlinear. --- Variétés de contact (Géométrie) --- Equations différentielles non linéaires --- Nonlinear differential equations --- Nonlinear theories --- Manifolds, Contact --- Almost contact manifolds --- Differentiable manifolds --- Geometry, Differential
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Statistique mathématique. --- Géométrie différentielle. --- Mathematical statistics. --- Geometry, Differential. --- Mathematical statistics --- Geometry, Differential --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- MSC 53-XX (2000) --- Systèmes différentiels involutifs --- Problème de Tammes --- Matrices de Stokes --- Équation de pullback --- Géométrie différentielle affine --- Espaces hamiltoniens --- Bernstein, Théorème de --- Anneaux déterminantiels --- Bochner, Technique de --- Calcul tensoriel --- Congruences (géométrie) --- Connexions (mathématiques) --- Coordonnées (mathématiques) --- Corps convexes --- Courbes --- Ensembles convexes --- Espaces à courbure constante --- Espaces généralisés --- Espaces symétriques --- Finsler, Espaces de --- Formes différentielles --- Formes extérieures (mathématiques) --- G-espaces --- G-structures --- Géodésiques (mathématiques) --- Géométrie différentielle globale --- Géométrie différentielle projective --- Géométrie intégrale --- Géométrie symplectique --- Groupes d'holonomie --- Hyperespace --- Lagrange, Espaces de --- Lie, Dérivées de --- Penrose, Transformation de --- Plateau, Problème de --- Quantification géométrique --- Réseaux tangentiels (géométrie différentielle) --- Riemann, Variétés de --- Géométrie de Riemann --- Sous-variétés (mathématiques) --- Structures hermitiennes --- Structures kählériennes --- Surfaces (mathématiques) --- Surfaces convexes --- Surfaces réglées --- Topologie différentielle --- Transformations (mathématiques) --- Variétés (mathématiques) --- Variétés de contact --- Variétés kählériennes --- Variétés quasi-complexes --- Variétés symplectiques --- Géométrie --- Inférence statistique --- Mathématiques --- Biométrie --- Échantillonnage --- Probabilités --- Statistique --- Sommes cumulées, Méthode des --- Analyse de régression --- Analyse de variance --- Analyse des données --- Analyse multivariée --- Analyse séquentielle --- Calcul d'erreur --- Carrés latins --- Comparaisons par paires, Méthode des --- Corrélation (statistique) --- Efficacité asymptotique (statistique) --- Estimation, Théorie de l' --- Fiabilité --- Fonctions pseudo-aléatoires --- Loi des grands nombres --- Modèles linéaires (statistique) --- Modèles non linéaires (statistique) --- Moindres carrés --- Physique statistique --- Plan d'expérience --- Prévision, Théorie de la --- Rang et sélection (statistique) --- Rupture (statistique) --- Séries chronologiques --- Statistique non paramétrique --- Statistiques robustes --- Tableaux de contingence --- Tests d'hypothèses (statistique) --- Statistique stellaire --- Differential geometry --- Statistical methods --- Méthodes statistiques --- statistique --- Differential geometry. Global analysis --- Géométrie différentielle --- Statistique mathématique
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