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- catalog abstract ""This text provides an introduction to basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas: for instance, the existence, uniqueness, and smoothness theorems for differential equations and the flow of a vector field; the basic theory of vector bundles including the existence of tubular neighborhoods for a submanifold; the calculus of differential forms; basic notions of symplectic manifolds, including the canonical 2-form; sprays and covariant derivatives for Riemannian and pseudo-Riemannian manifolds; and applications to the exponential map, including the Cartan-Hadamard theorem and the first basic theorem of calculus of variations."--BOOK JACKET.".
- catalog contributor b11077384.
- catalog created "1999.".
- catalog date "1999".
- catalog date "1999.".
- catalog dateCopyrighted "1999.".
- catalog description ""This text provides an introduction to basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas: for instance, the existence, uniqueness, and smoothness theorems for differential equations and the flow of a vector field; the basic theory of vector bundles including the existence of tubular neighborhoods for a submanifold; the calculus of differential forms; basic notions of symplectic manifolds, including the canonical 2-form; sprays and covariant derivatives for Riemannian and pseudo-Riemannian manifolds; and applications to the exponential map, including the Cartan-Hadamard theorem and the first basic theorem of calculus of variations."--BOOK JACKET.".
- catalog description "I: General Differential Theory -- Differential Calculus -- Manifolds -- Vector Bundles -- Vector Fields And Differential Equations -- Operations On Vector Fields And Differential Forms -- The Theorem Of Frobenius -- II: Metrics, Covariant Derivatives And Riemannian Geometry -- Metrics -- Covariant Derivatives And Geodesics -- Curvature -- Jacobi Lifts And Tensorial Splitting Of The Double Tangent Bundle -- Curvature And The Variation Formula -- An Example Of Seminegative Curvature -- Automorphisms And Symmetries -- Immersions and Submersions -- III: Volume Forms And Integration -- Volume Forms -- Integration Of Differential Forms -- Stokes' Theorem -- Applications Of Stokes' Theorem -- Appendix: The Spectral Theorem.".
- catalog description "Includes bibliographical references and index.".
- catalog extent "xvii, 535 p. :".
- catalog identifier "038798593X (alk. paper)".
- catalog isPartOf "Graduate texts in mathematics ; 191".
- catalog issued "1999".
- catalog issued "1999.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "516.3/6 21".
- catalog subject "Geometry, Differential.".
- catalog subject "QA641 .L33 1999".
- catalog tableOfContents "I: General Differential Theory -- Differential Calculus -- Manifolds -- Vector Bundles -- Vector Fields And Differential Equations -- Operations On Vector Fields And Differential Forms -- The Theorem Of Frobenius -- II: Metrics, Covariant Derivatives And Riemannian Geometry -- Metrics -- Covariant Derivatives And Geodesics -- Curvature -- Jacobi Lifts And Tensorial Splitting Of The Double Tangent Bundle -- Curvature And The Variation Formula -- An Example Of Seminegative Curvature -- Automorphisms And Symmetries -- Immersions and Submersions -- III: Volume Forms And Integration -- Volume Forms -- Integration Of Differential Forms -- Stokes' Theorem -- Applications Of Stokes' Theorem -- Appendix: The Spectral Theorem.".
- catalog title "Fundamentals of differential geometry / Serge Lang.".
- catalog type "text".