000			04107nam a22004575i 4500
999			_c387527 _d387527
001			387527
003			ES-MaUEC
005			20230322175434.0
006			a||||fo|||| 00| 0
007			cr nn 008mamaa
008			220601s2019 sz | s |||| 0|eng d
020			_a9783031024160
024	7		_a10.1007/978-3-031-02416-0 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC _dES-MaUEC
050		4	_aQA641 _b2019 EB
100	1		_aCalviño-Louzao, Esteban _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9687521
245	1	0	_aAspects of Differential Geometry IV _cby Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo
250			_a1st edition 2019
264		1	_aCham _bSpringer International Publishing _c2019
300			_a1 recurso en línea (XVII, 149 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 -- An Introduction to Affine Geometry -- The Geometry of Type A Models -- The Geometry of Type B Models -- Applications of Affine Surface Theory -- Bibliography -- Authors' Biographies -- Index .
520			_aBook IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces {which} are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2. The translation group ℝ² is Abelian and the �������� + ���� group\index{ax+b group} is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type ���� surfaces. These are the left-invariant affine geometries on ℝ². Associating to each Type ���� surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue ����=-1$ turns out to be a very powerful technique and plays a central role in our study as it links an analytic invariant with the underlying geometry of the surface. The third chapter deals with Type ���� surfaces; these are the left-invariant affine geometries on the �������� + ���� group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere ����². The fourth chapter presents relations between the geometry of an affine surface and the geometry of the cotangent bundle equipped with the neutral signature metric of the modified Riemannian extension.
988			_aSynthesis Collection of Technology_2019
650		7	_2embne _9140354 _aGeometría diferencial
700	1		_aGarcía-Río, Eduardo _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9687522
700	1		_aGilkey, Peter B. _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9686447
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: _z9783031002625
776	0	8	_iPrinted edition: _z9783031012884
776	0	8	_iPrinted edition: _z9783031035449
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-02416-0 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b03/2023 _dz _esc _zSI