000			01570cam a2200229 a 4500
008			970417s1997 nyua b 001 0 eng
020			_a9780387983226
082	0	0	_a516.373 _bLEE
100	1		_aLee, John M.
245	1	0	_aRiemannian manifolds: an introduction to curvature
260			_aNew York: _bSpringer, _c1997.
300			_a 224 p.: _bill.; _c24 cm.
365			_aINR _b1610.77
440		0	_aGraduate texts in mathematics; vol.176
504			_aIncludes bibliographical references and index.
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.
650		0	_aRiemannian manifolds
650		0	_aCurvature
650		0	_aRiemannian metrics
650		0	_aBonnet theorem
942			_cTD
999			_c44513 _d44513