000			02894nam a2200361 i 4500
008			970417s1997 nyua b 001 0 eng
010			_a97014537
020			_a038798271X _qhardcover : acid-free paper
020			_a9780387982717 _qhardcover : acid-free paper
020			_a0387983228 _qsoftcover : acid-free paper
020			_a9780387983226 _qsoftcover : acid-free paper
040			_aDLC _beng _cDLC _dOHX _dUBA _dMUQ _dBAKER _dNLGGC _dBTCTA _dYDXCP _dOCLCG _dUAB _dZWZ _dDEBSZ _dBDX _dOCLCO _dOCLCF _dBAUN _erda
049			_aBAUN_MERKEZ
050	0	4	_aQA649 _b.L397 1997
100	1		_aLee, John M., _d1950-
245	1	0	_aRiemannian manifolds : _ban introduction to curvature / _cJohn M. Lee.
264		1	_aNew York : _bSpringer, _c[1997]
264		4	_c©1997
300			_axv, 224 pages : _billustrations ; _c24 cm.
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aGraduate texts in mathematics ; _v176
504			_aIncludes bibliographical references (pages [209]-211) and index.
505	0	0	_t1. What Is Curvature? _t-- 2. Review of Tensors, Manifolds, and Vector Bundles _t-- 3. Definitions and Examples of Riemannian Metrics _t-- 4. Connections _t-- 5. Riemannian Geodesics _t-- 6. Geodesics and Distance _t-- 7. Curvature _t-- 8. Riemannian Submanifolds _t-- 9. The Gauss-Bonnet Theorem _t-- 10. Jacobi Fields _t-- 11. Curvature and Topology.
520			_aThis text is designed for a one-quarter or one-semester graduate course on 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 study of Riemannian manifolds. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics, and then introduces the curvature tensor as a way of measuring whether a Riemannian manifold is locally equivalent to Euclidean space. Submanifold theory is developed next 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 the characterization of manifolds of constant curvature.
520	8		_aThis unique volume will appeal especially to students by presenting a selective introduction to the main ideas 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.
650		0	_aRiemannian manifolds.
830		0	_919347 _aGraduate texts in mathematics ; _v176.
900			_a19989
900			_bSatın
942			_2lcc _cKT
999			_c16829 _d16829