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OverviewFull Product DetailsAuthor: Serge LangPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 1st ed. 1999. Corr. 2nd printing 2001 Volume: 191 Dimensions: Width: 15.50cm , Height: 3.10cm , Length: 23.50cm Weight: 2.130kg ISBN: 9780387985930ISBN 10: 038798593 Pages: 540 Publication Date: 30 December 1998 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Awaiting stock  The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you. Table of ContentsI General Differential Theory.- I Differential Calculus.- II Manifolds.- III Vector Bundles.- IV Vector Fields and Differential Equations.- V Operations on Vector Fields and Differential Forms.- VI The Theorem of Frobenius.- II Metrics, Covariant Derivatives, and Riemannian Geometry.- VII Metrics.- VIII Covariant Derivatives and Geodesics.- IX Curvature.- X Jacobi Lifts and Tensorial Splitting of the Double Tangent Bundle.- XI Curvature and the Variation Formula.- XII An Example of Seminegative Curvature.- XIII Automorphisms and Symmetries.- XIV Immersions and Submersions.- III Volume Forms and Integration.- XV Volume Forms.- XVI Integration of Differential Forms.- XVII Stokes’ Theorem.- XVIII Applications of Stokes’ Theorem.Reviews"""There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books. ... It can be warmly recommended to a wide audience."" EMS Newsletter, Issue 41, September 2001 ""The text provides a valuable introduction to basic concepts and fundamental results in differential geometry. A special feature of the book is that it deals with infinite-dimensional manifolds, modeled on a Banach space in general, and a Hilbert space for Riemannian geometry. The set-up works well on basic theorems such as the existence, uniqueness and smoothness theorem for differential equations and the flow of a vector field, existence of tubular neighborhoods for a submanifold, and the Cartan-Hadamard theorem. A major exception is the Hopf-Rinow theorem. Curvature and basic comparison theorems are discussed. In the finite-dimensional case, volume forms, the Hodge star operator, and integration of differentialforms are expounded. The book ends with the Stokes theorem and some of its applications.""-- MATHEMATICAL REVIEWS" There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books. ... It can be warmly recommended to a wide audience. EMS Newsletter, Issue 41, September 2001 The text provides a valuable introduction to basic concepts and fundamental results in differential geometry. A special feature of the book is that it deals with infinite-dimensional manifolds, modeled on a Banach space in general, and a Hilbert space for Riemannian geometry. The set-up works well on basic theorems such as the existence, uniqueness and smoothness theorem for differential equations and the flow of a vector field, existence of tubular neighborhoods for a submanifold, and the Cartan-Hadamard theorem. A major exception is the Hopf-Rinow theorem. Curvature and basic comparison theorems are discussed. In the finite-dimensional case, volume forms, the Hodge star operator, and integration of differential forms are expounded. The book ends with the Stokes theorem and some of its applications. -- MATHEMATICAL REVIEWS There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books. ...<br>It can be warmly recommended to a wide audience. <br>EMS Newsletter, Issue 41, September 2001 <p> The text provides a valuable introduction to basic concepts and fundamental results in differential geometry. A special feature of the book is that it deals with infinite-dimensional manifolds, modeled on a Banach space in general, and a Hilbert space for Riemannian geometry. The set-up works well on basic theorems such as the existence, uniqueness and smoothness theorem for differential equations and the flow of a vector field, existence of tubular neighborhoods for a submanifold, and the Cartan-Hadamard theorem. A major exception is the Hopf-Rinow theorem. Curvature and basic comparison theorems are discussed. In the finite-dimensional case, volume forms, the Hodge star operator, and integration of differential forms are expounded. The book ends with the Stokes theorem and some of its applications. -- MATHEMATICAL REVIEWS Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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