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008			230419s2015 sz | s |||| 0|eng d
020			_a9783031024085
024	7		_a10.1007/978-3-031-02408-5 _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 II _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, 143 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 -- Additional Topics in Riemannian Geometry -- de Rham Cohomology -- Lie Groups -- Homogeneous Spaces and Symmetric Spaces -- Other Cohomology Theories -- 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. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups and the Peter--Weyl Theorem are treated. In Chapter 7, material concerning homogeneous spaces and symmetric spaces is presented. Book II concludes in Chapter 8 where the relationship between simplicial cohomology, singular cohomology, sheaf cohomology, and de Rham cohomology is established. 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 total curvature and length of curves given by a single ODE is new as is the discussion of the total Gaussian curvature of a surface defined by a pair of ODEs.
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: _z9783031012808
776	0	8	_iPrinted edition: _z9783031035364
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-02408-5 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b04/2023 _dz _eIG _zSI