000 | 04347nam a22005655i 4500 | ||
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001 | 978-3-031-02416-0 | ||
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007 | cr nn 008mamaa | ||
008 | 220601s2019 sz | s |||| 0|eng d | ||
020 |
_a9783031024160 _9978-3-031-02416-0 |
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024 | 7 |
_a10.1007/978-3-031-02416-0 _2doi |
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100 | 1 |
_aCalviño-Louzao, Esteban. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _981241 |
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245 | 1 | 0 |
_aAspects of Differential Geometry IV _h[electronic resource] / _cby Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo. |
250 | _a1st ed. 2019. | ||
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2019. |
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300 |
_aXVII, 149 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751 |
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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. | ||
650 | 0 |
_aMathematics. _911584 |
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650 | 0 |
_aStatistics . _931616 |
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650 | 0 |
_aEngineering mathematics. _93254 |
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650 | 1 | 4 |
_aMathematics. _911584 |
650 | 2 | 4 |
_aStatistics. _914134 |
650 | 2 | 4 |
_aEngineering Mathematics. _93254 |
700 | 1 |
_aGarcía-Río, Eduardo. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _981242 |
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700 | 1 |
_aGilkey, Peter. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _981243 |
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700 | 1 |
_aPark, JeongHyeong. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _981244 |
|
700 | 1 |
_aVázquez-Lorenzo, Ramón. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _981245 |
|
710 | 2 |
_aSpringerLink (Online service) _981246 |
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773 | 0 | _tSpringer Nature eBook | |
776 | 0 | 8 |
_iPrinted edition: _z9783031002625 |
776 | 0 | 8 |
_iPrinted edition: _z9783031012884 |
776 | 0 | 8 |
_iPrinted edition: _z9783031035449 |
830 | 0 |
_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751 _981247 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-02416-0 |
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