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008			081109s1997 enka | 001 0 eng d
020			_a038798271x
020			_a0387983228 pbk
039		9	_a201402040058 _bVLOAD _c201008020901 _dmalmash _c200811101434 _dvenkatrajand _c200811091033 _dNoora _y200811091027 _zNoora
050			_aQA649 _b.L397 1997
100	1		_aLee, John M., _d1950- _932088
245	1	0	_aRiemannian Manifolds : _bAn Introduction to curvature : with 88 illustrations / _cJohn M. Lee.
260			_aNew York; _aLondon : _bSpringer, _cc1997.
300			_axv, 224 p : _bill ; _c25 cm.
440		0	_aGraduate texts in mathematics ; _v176 _91563
504			_aBibliography: p209-211. - Includes index.
505			_aWhat 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.
520			_aThis text is designed for a one-quarter or one-semester graduate course in Riemannian geometry. It 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. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics, and then introduces the Riemann curvature tensor, before movsub manifoldsubmanifold theory, in order to give the curvature tensor a concrete quantitative interpretation. The remainder of the text is devoted to 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. This unique volume will especially appeal to students by presenting a selective introduction to the main ides of the subject in an easily accessible way. The material is ideal for a single course, but broad enough to provide students with a firm foundation from which to pursue research or develop applications in Riemannian geometry and other fields that use its tools. Of special interest are the 'exercises' and 'problems' dispersed throughout the text. The exercises are carefully chosen and timed so as to give the reader opportunities to review mathas justhat hasjust been introduced, to practice working with the definitions, and to develop skills that are used later in the book. The problems that conclude the chapters are generally more difficult. They not only intmaterialew mateiral not covered in the body of the text, but they also provide the students with indispensable practice in using the
650		0	_aRiemannian manifolds. _943676
942			_2lcc _n0 _cBK
999			_c23232 _d23232