| 000 | 02261cam a22002414a 4500 | ||
|---|---|---|---|
| 001 | vtls000001748 | ||
| 003 | VRT | ||
| 005 | 20250102224908.0 | ||
| 008 | 081109s2004 nyu |b 001 0 eng | ||
| 020 | _a038720430X (acidfree paper) | ||
| 039 | 9 |
_a201402040056 _bVLOAD _c201007191037 _dmalmash _c200811101454 _dvenkatrajand _c200811091250 _dNoora _y200811091249 _zNoora |
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| 050 | 0 | 0 |
_aQA641 _b.W327 2004 |
| 100 | 1 |
_aWalschap, Gerard, _d1954- _949173 |
|
| 245 | 1 | 0 |
_aMetric Sructures in Differential Geometry / _cGerard Walschap. |
| 260 |
_aNew York : _bSpringer, _cc2004. |
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| 300 |
_aviii, 226 p. ; _c25 cm. |
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| 440 | 0 |
_aGraduate texts in mathematics ; _v224 _91563 |
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| 504 | _aIncludes bibliographical references (p. 221-222) and index. | ||
| 505 | _aPreface.- Differentiable manifolds.- Fiber bundles.- Homotopy groups and bundles over spheres.- Connections and curvature.- Metric structures.- Characteristic classes.- Bibliography.- Index. | ||
| 520 | _aThis text is an introduction to the theory of differentiable manifolds and fiber bundles. The only requisites are a solid background in calculus and linear algebra, together with some basic point-set topology. The first chapter provides a comprehensive overview of differentiable manifolds. The following two chapters are devoted to fiber bundles and homotopy theory of fibrations. Vector bundles have been emphasized, although principal bundles are also discussed in detail. The last three chapters study bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres. Chapter 5, with its focus on the tangent bundle, also serves as a basic introduction to Riemannian geometry in the large. This book can be used for a one-semester course on manifolds or bundles, or a two-semester course in differential geometry.Gerard Walschap is Professor of Mathematics at the University of Oklahoma where he developed this book for a series of graduate courses he has taught over the past few years. | ||
| 650 | 0 |
_aGeometry, Differential. _9904 |
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| 942 |
_2lcc _n0 _cBK |
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| 999 |
_c23240 _d23240 |
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