# Differential and Riemannian Manifolds (Graduate Texts in Mathematics)

## Serge Lang

3,8 valoración promedio
( 5 valoraciones por Goodreads )

This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.).

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From the Back Cover:

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.

Review:

S. Lang

Differential and Riemannian Manifolds

"An introduction to differential geometry, starting from recalling differential calculus and going through all the basic topics such as manifolds, vector bundles, vector fields, the theorem of Frobenius, Riemannian metrics and curvature. Useful to the researcher wishing to learn about infinite-dimensional geometry."

―MATHEMATICAL REVIEWS

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## 1.Differential and Riemannian Manifolds

Editorial: Springer-Verlag New York Inc. (1996)
ISBN 10: 0387943382 ISBN 13: 9780387943381
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Descripción Springer-Verlag New York Inc., 1996. HRD. Estado de conservación: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IP-9780387943381

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## 2.Differential and Riemannian Manifolds (Hardback)

Editorial: Springer-Verlag New York Inc., United States (1996)
ISBN 10: 0387943382 ISBN 13: 9780387943381
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Descripción Springer-Verlag New York Inc., United States, 1996. Hardback. Estado de conservación: New. 3rd ed. 1995. Corr. 2nd printing 1996. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.). Nº de ref. de la librería LIE9780387943381

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## 3.Differential and Riemannian Manifolds (Graduate Texts in Mathematics)

Editorial: Springer (1996)
ISBN 10: 0387943382 ISBN 13: 9780387943381
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Descripción Springer, 1996. Estado de conservación: New. This item is printed on demand for shipment within 3 working days. Nº de ref. de la librería LP9780387943381

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## 4.Differential and Riemannian Manifolds

Editorial: Springer (2016)
ISBN 10: 0387943382 ISBN 13: 9780387943381
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Descripción Springer, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9780387943381_lsuk

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## 5.Differential and Riemannian Manifolds

Editorial: Springer (1995)
ISBN 10: 0387943382 ISBN 13: 9780387943381
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Descripción Springer, 1995. Hardback. Estado de conservación: NEW. 9780387943381 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0275391

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## 6.Differential and Riemannian Manifolds

Editorial: Springer-Verlag New York Inc. (1996)
ISBN 10: 0387943382 ISBN 13: 9780387943381
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Descripción Springer-Verlag New York Inc., 1996. HRD. Estado de conservación: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Nº de ref. de la librería IP-9780387943381

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## 7.Differential and Riemannian Manifolds (Graduate Texts in Mathematics)

Editorial: Springer (2017)
ISBN 10: 0387943382 ISBN 13: 9780387943381
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Descripción Springer, 2017. Hardcover. Estado de conservación: New. Never used! This item is printed on demand. Nº de ref. de la librería 0387943382

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## 8.Differential and Riemannian Manifolds (Graduate Texts in Mathematics)

ISBN 10: 0387943382 ISBN 13: 9780387943381
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Descripción Estado de conservación: New. Nº de ref. de la librería ria9780387943381_ing

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## 9.Differential and Riemannian Manifolds (Graduate Texts in Mathematics)

Editorial: Springer (1996)
ISBN 10: 0387943382 ISBN 13: 9780387943381
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Descripción Springer, 1996. Hardcover. Estado de conservación: New. This item is printed on demand. Nº de ref. de la librería INGM9780387943381

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## 10.Differential and Riemannian Manifolds (Graduate Texts in Mathematics)

Editorial: Springer (1996)
ISBN 10: 0387943382 ISBN 13: 9780387943381
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Irish Booksellers
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Descripción Springer, 1996. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería M0387943382

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