Descripción de contraportada
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; applications to the exponential map, including the Cartan-Hadamard theorem, and the first basic theorem of calculus of variations. These are all covered for infinite-dimensional manifolds, modeled on Banach and Hilbert spaces, at no cost in complications, and some gain in the elegance of the proofs. In the finite-dimensional case, differential forms of top degree are discussed, leading to Stokes' theorem (even for manifolds with singular boundary), and several of its applications to the differential or Riemannian case.
Detalles
- Título Differential and Riemannian Manifolds
- Autor Serge Lang
- Encuadernación Tapa dura
- Edición 3rd
- Páginas 364
- Volúmenes 1
- Idioma ENG
- Editorial Springer, New York
- Fecha de publicación 1995-03-09
- Ilustrado Sí
- Features Illustrated, Maps
- ISBN 9780387943381 / 0387943382
- Peso 1.62 libras (0.73 kg)
- Dimensiones 9.53 x 6.4 x 0.91 pulgadas (24.21 x 16.26 x 2.31 cm)
- Library of Congress subjects Riemannian manifolds, Differentiable manifolds
- Número de catálogo de la Librería del Congreso de EEUU 95001594
- Dewey Decimal Code 516.36
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Differential and Riemannian Manifolds
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