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Riemannian Manifolds

An Introduction to Curvature

John M. Lee (Autor)

Buch | Softcover

226 Seiten

1997 | 1997 ed.
Springer-Verlag New York Inc.
978-0-387-98322-6 (ISBN)

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This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

What Is Curvature?.- Review of Tensors, Manifolds, and Vector Bundles.- Definitions and Examples of Riemannian Metrics.- Connections.- Riemannian Geodesics.- Geodesics and Distance.- Curvature.- Riemannian Submanifolds.- The Gauss-Bonnet Theorem.- Jacobi Fields.- Curvature and Topology.

Erscheint lt. Verlag	5.9.1997
Reihe/Serie	Graduate Texts in Mathematics ; 176
Zusatzinfo	XV, 226 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Gewicht	790 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Themenwelt	Naturwissenschaften ► Physik / Astronomie
ISBN-10	0-387-98322-8 / 0387983228
ISBN-13	978-0-387-98322-6 / 9780387983226
Zustand	Neuware