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- catalog abstract ""This book treats that part of Riemannian geometry related to more classical topics in a very original, clear and solid style. Before going to Riemannian geometry, the author presents a more general theory of manifolds with a linear connection. Having in mind different generalizations of Riemannian manifolds, it is clearly stressed which notions and theorems belong to Riemannian geometry and which of them are of a more general nature. Much attention is paid to transformation groups of smooth manifolds." "Throughout the book, different aspects of symmetric spaces are treated. The author combines the co-ordinate and invariant approaches to differential geometry, which give the reader tools for practical calculations as well as a theoretical understanding of the subject. The book contains a large appendix on foundations of differentiable manifolds and basic structures on them which makes it self-contained and practically independent from other sources." "The results are well presented and useful for students in mathematics and theoretical physics, and for experts in these fields. The book can serve as a textbook for students doing geometry, as well as a references book for professional mathematicians and physicists."--Jacket.".
- catalog alternative "Riemannian geometry".
- catalog alternative "Rimanova geometriya. English.".
- catalog contributor b12200361.
- catalog created "c2001.".
- catalog date "2001".
- catalog date "c2001.".
- catalog dateCopyrighted "c2001.".
- catalog description ""This book treats that part of Riemannian geometry related to more classical topics in a very original, clear and solid style. Before going to Riemannian geometry, the author presents a more general theory of manifolds with a linear connection. Having in mind different generalizations of Riemannian manifolds, it is clearly stressed which notions and theorems belong to Riemannian geometry and which of them are of a more general nature. Much attention is paid to transformation groups of smooth manifolds." "Throughout the book, different aspects of symmetric spaces are treated. The author combines the co-ordinate and invariant approaches to differential geometry, which give the reader tools for practical calculations as well as a theoretical understanding of the subject. The book contains a large appendix on foundations of differentiable manifolds and basic structures on them which makes it self-contained and practically independent from other sources." "The results are well presented and useful for students in mathematics and theoretical physics, and for experts in these fields. The book can serve as a textbook for students doing geometry, as well as a references book for professional mathematicians and physicists."--Jacket.".
- catalog description "Affine connections -- Covariant diffetentiation curvature -- Affine mappings submanifolds -- Structural equations. Local symmetries -- Symmetric spaces -- Connections on lie groups -- Lie functor -- Affine fields and related topics -- Cartan theorem -- Palais and kobayashi theorems -- Lagrangians in riemannian spaces -- Metric properties of geodesics -- Harmonic functionals and related topics -- Manimal surfaces -- Curvature in riemannian space -- gaussian curvature -- Some special tensors -- Surfaces with conformal structure -- Mappings and submanifolds I -- Submanifolds II -- Fundamental forms of a hypersurface -- Spaces of constant curvature -- Space forms -- Four-dimensional manifolds -- Metrics on a lie group I -- Metrics on a lie group II -- Jacobi theory -- Some additional theorems I -- Some additional theorems II -- Smooth manifolds -- Tangent vectors -- Submanifolds of a smooth manifold -- Vector and tensor fields. Differential forms -- Vector bundles -- Connections on vector bundles -- Curvature tensor.".
- catalog description "Includes bibliographical references and index.".
- catalog extent "xviii, 503 p. : 24 cm.".
- catalog identifier "3540411089".
- catalog isPartOf "Encyclopaedia of mathematical sciences ; v. 91".
- catalog issued "2001".
- catalog issued "c2001.".
- catalog language "eng rus".
- catalog language "eng".
- catalog publisher "Berlin ; London : Springer,".
- catalog subject "Geometry, Riemannian.".
- catalog subject "QA649 .P67 2001".
- catalog tableOfContents "Affine connections -- Covariant diffetentiation curvature -- Affine mappings submanifolds -- Structural equations. Local symmetries -- Symmetric spaces -- Connections on lie groups -- Lie functor -- Affine fields and related topics -- Cartan theorem -- Palais and kobayashi theorems -- Lagrangians in riemannian spaces -- Metric properties of geodesics -- Harmonic functionals and related topics -- Manimal surfaces -- Curvature in riemannian space -- gaussian curvature -- Some special tensors -- Surfaces with conformal structure -- Mappings and submanifolds I -- Submanifolds II -- Fundamental forms of a hypersurface -- Spaces of constant curvature -- Space forms -- Four-dimensional manifolds -- Metrics on a lie group I -- Metrics on a lie group II -- Jacobi theory -- Some additional theorems I -- Some additional theorems II -- Smooth manifolds -- Tangent vectors -- Submanifolds of a smooth manifold -- Vector and tensor fields. Differential forms -- Vector bundles -- Connections on vector bundles -- Curvature tensor.".
- catalog title "Geometry VI : Riemannian geometry / M.M. Postnikov.".
- catalog title "Riemannian geometry".
- catalog title "Rimanova geometriya. English.".
- catalog type "text".