000			03790cam a22004335i 4500
001			21680999
003			OSt
005			20240528120356.0
006			m |o d |
007			cr |||||||||||
008			171013s2017 gw |||| o |||| 0|eng
010			_a 2019747258
020			_a9783319618593 (Pbk)
024	7		_a10.1007/978-3-319-61860-9 _2doi
035			_a(DE-He213)978-3-319-61860-9
040			_aDLC _beng _epn _erda _cIISERB
072		7	_aMAT012030 _2bisacsh
072		7	_aPBMP _2bicssc
072		7	_aPBMP _2thema
082	0	4	_a516.36 J79R7 _223
100	1		_aJost, Jürgen. _930272
245	1	0	_aRiemannian Geometry and Geometric Analysis _cby Jürgen Jost.
250			_a7th ed. 2017.
260			_aSwitzarland: _bSpringer Nature, _c2017.
300			_aXIV, 697 pages 19 illustrations, 4 illustrations in color.
490	1		_aUniversitext, _x0172-5939
505	0		_a1 Riemannian Manifolds -- 2 Lie Groups and Vector Bundles -- 3 The Laplace Operator and Harmonic Differential Forms -- 4 Connections and Curvature -- 5 Geometry of Submanifolds -- 6 Geodesics and Jacobi Fields -- A Short Survey on Curvature and Topology -- 7 Symmetric Spaces and Kähler Manifolds -- 8 Morse Theory and Floer Homology -- 9 Harmonic Maps between Riemannian Manifolds -- 10 Harmonic Maps from Riemann Surfaces -- 11 Variational Problems from Quantum Field Theory -- A Linear Elliptic Partial Differential Equations -- B Fundamental Groups and Covering Spaces -- Bibliography -- Index.
520			_aThis established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome." Mathematical Reviews "For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained ... The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field." Monatshefte für Mathematik.
650		0	_aDifferential geometry. _930273
650		0	_aMathematical physics. _930274
650	1	4	_aDifferential Geometry. _930275
650	2	4	_aTheoretical, Mathematical and Computational Physics. _930276
776	0	8	_iPrint version: _tRiemannian geometry and geometric analysis _z9783319618593 _w(DLC) 2017950288
776	0	8	_iPrinted edition: _z9783319618593
776	0	8	_iPrinted edition: _z9783319618616
830		0	_aUniversitext, _930277
906			_a0 _bibc _corigres _du _encip _f20 _gy-gencatlg
942			_2ddc _cBK
999			_c10320 _d10320