# Fundamentals of Differential Geometry

## Lang, Serge

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This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the 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." --EMS NEWSLETTER

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Recensione:

"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

Contenuti:

I: GENERAL DIFFERENTIAL THEORY. 1: Differential Calculus. 2: Manifolds. 3: Vector Bundles. 4: Vector Fields and Differential Equations. 5: Operations on Vector Fields and Differential Forms. 6: The Theorem of Frobenius. II: METRICS, COVARIANT DERIVATIVES AND RIEMANNIAN GEOMETRY. 7: Metrics. 8: Covariant Derivatives and Geodesics. 9: Curvature. 10: Jacobi Lifts and Tensorial Splitting of the Double Tangent Bundle. 11: Curvature and the Variation Formula. 12: An Example of Seminegative Curvature. 13: Automorphisms and Symmetries. III: VOLUME FORMS AND INTEGRATION. 15: Volume Forms. 16: Integration of Differential Forms. 17: Stokes' Theorem. 18: Applications of Stokes' Theorem. Appendix: The Spectral Theorem.

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## 1.Fundamentals of Differential Geometry (Hardback)

Editore: Springer-Verlag New York Inc., United States (2001)
ISBN 10: 038798593X ISBN 13: 9780387985930
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Descrizione libro Springer-Verlag New York Inc., United States, 2001. Hardback. Condizione libro: New. 1st ed. 1999. Corr. 2nd printing 2001. 236 x 162 mm. Language: English . Brand New Book. This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the 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. --EMS NEWSLETTER. Codice libro della libreria LIB9780387985930

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## 2.Fundamentals of Differential Geometry

Editore: Springer-Verlag New York Inc. 2001-09-21, New York, NY (2001)
ISBN 10: 038798593X ISBN 13: 9780387985930
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Descrizione libro Springer-Verlag New York Inc. 2001-09-21, New York, NY, 2001. hardback. Condizione libro: New. Codice libro della libreria 9780387985930

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## 3.Fundamentals of Differential Geometry (Hardback)

Editore: Springer-Verlag New York Inc., United States (2001)
ISBN 10: 038798593X ISBN 13: 9780387985930
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Descrizione libro Springer-Verlag New York Inc., United States, 2001. Hardback. Condizione libro: New. 1st ed. 1999. Corr. 2nd printing 2001. 236 x 162 mm. Language: English . Brand New Book. This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the 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. --EMS NEWSLETTER. Codice libro della libreria LIB9780387985930

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## 4.Fundamentals of Differential Geometry (Graduate Texts in Mathematics)

Editore: Springer (2001)
ISBN 10: 038798593X ISBN 13: 9780387985930
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Descrizione libro Springer, 2001. Condizione libro: New. Codice libro della libreria L9780387985930

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## 5.Fundamentals of Differential Geometry

Editore: Springer-Verlag New York Inc. (2001)
ISBN 10: 038798593X ISBN 13: 9780387985930
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Descrizione libro Springer-Verlag New York Inc., 2001. HRD. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I1-9780387985930

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## 6.Fundamentals of Differential Geometry

Editore: Springer (1998)
ISBN 10: 038798593X ISBN 13: 9780387985930
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Descrizione libro Springer, 1998. Hardback. Condizione libro: NEW. 9780387985930 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0276758

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## 7.Fundamentals of Differential Geometry (Graduate Texts in Mathematics)

Editore: Springer (1998)
ISBN 10: 038798593X ISBN 13: 9780387985930
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Descrizione libro Springer, 1998. Hardcover. Condizione libro: New. Corrected. This item is printed on demand. Codice libro della libreria DADAX038798593X

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## 8.Fundamentals of Differential Geometry (Graduate Texts in Mathematics)

Editore: Springer (2001)
ISBN 10: 038798593X ISBN 13: 9780387985930
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Descrizione libro Springer, 2001. Hardcover. Condizione libro: New. book. Codice libro della libreria 038798593X

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## 9.Fundamentals of Differential Geometry

Editore: Springer Sep 2001 (2001)
ISBN 10: 038798593X ISBN 13: 9780387985930
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Descrizione libro Springer Sep 2001, 2001. Buch. Condizione libro: Neu. 235x155x36 mm. Neuware - This is the new edition of Serge Lang's 'Differential and Riemannian Manifolds.' 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. 564 pp. Englisch. Codice libro della libreria 9780387985930

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## 10.Fundamentals of Differential Geometry

Editore: Springer (2016)
ISBN 10: 038798593X ISBN 13: 9780387985930
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Descrizione libro Springer, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780387985930_lsuk

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