000			03242nam a2200325Ia 4500
003			OSt
005			20250125144536.0
008			241112s9999 xx 000 0 und d
020			_a9783030801069 (pbk.) _c€ 49.99
040			_bENG _cIISER-BPR
041			_aENG
082			_a516.362 _bLEE _223rd
100			_aLee, John M. _91072
222			_aMathematics
245		0	_aIntroduction to riemannian manifolds
250			_a2nd ed.
260			_aCham, Switzerland: _bSpringer Nature, _cc2021.
300			_axiii, 437p. : _bill. ; _c24cm
440			_aGraduate Texts in Mathematics _vVol. 176 _92610
504			_aIncludes appendices, bibliographic references, notation index and subject index.
520			_aThis textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee’s earlier book, Riemannian Manifolds: An Introduction to Curvature. Numerous exercises and problem sets provide the student with opportunities to practice and develop skills; appendices contain a brief review of essential background material. While demonstrating the uses of most of the main technical tools needed for a careful study of Riemannian manifolds, this text focuses on ensuring that the student develops an intimate acquaintance with the geometric meaning of curvature. The reasonably broad coverage begins with a treatment of indispensable tools for working with Riemannian metrics such as connections and geodesics. Several topics have been added, including an expanded treatment of pseudo-Riemannianmetrics, a more detailed treatment of homogeneous spaces and invariant metrics, a completely revamped treatment of comparison theory based on Riccati equations, and a handful of new local-to-global theorems, to name just a few highlights. Reviews of the first edition: Arguments and proofs are written down precisely and clearly. The expertise of the author is reflected in many valuable comments and remarks on the recent developments of the subjects. Serious readers would have the challenges of solving the exercises and problems. The book is probably one of the most easily accessible introductions to Riemannian geometry. (M.C. Leung, MathReview) The book’s aim is to develop tools and intuition for studying the central unifying theme in Riemannian geometry, which is the notion of curvature and its relation with topology. The main ideas of the subject, motivated as in the original papers, are introduced here in an intuitive and accessible way…The book is an excellent introduction designed for a one-semester graduate course, containing exercises and problems which encourage students to practice working with the new notions and develop skills for later use. By citing suitable references for detailed study, the reader is stimulated to inquire into further research. (C.-L. Bejan, zBMATH)
650			_aMathematics _92611
650			_aGeometry _92612
650			_aDifferential geometry _92613
650			_aRiemannian manifolds _92614
942			_cBK _2ddc
942			_2ddc
947			_a4581.583500000001
948			_a22
999			_c4212 _d4212