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007			cr nn 008mamaa
008			220601s2015 sz | o |||| 0|eng d
020			_a9783031024078
024	7		_a10.1007/978-3-031-02407-8 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC _dES-MaUEC
050		4	_aQA641 _b2015 EB
100	1		_aGilkey, Peter B. _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9686447
245	1	0	_aAspects of Differential Geometry _nI _cby Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo
250			_a1st edition 2015
264		1	_aCham _bSpringer International Publishing _c2015
300			_a1 recurso en línea (XIII, 140 páginas)
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
490	0		_aSynthesis Lectures on Mathematics & Statistics _x1938-1751
505	0		_aPreface -- Acknowledgments -- Basic Notions and Concepts -- Manifolds -- Riemannian and Pseudo-Riemannian Geometry -- Bibliography -- Authors' Biographies -- Index .
520			_aDifferential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new. Table of Contents: Preface / Acknowledgments / Basic Notions and Concepts / Manifolds / Riemannian and Pseudo-Riemannian Geometry / Bibliography / Authors' Biographies / Index.
988			_aSynthesis Collection of Technology_2015
650		7	_2embne _9140354 _aGeometría diferencial
700	1		_aPark, Jeonghyeong _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9686448
700	1		_aVázquez-Lorenzo, Ramón _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9686449
776	0	8	_iPrinted edition: _z9783031012792
776	0	8	_iPrinted edition: _z9783031035357
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-02407-8 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b02/2023 _dz _eb _zSI