000 | 05267nam a2200709 i 4500 | ||
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001 | 8694982 | ||
003 | IEEE | ||
005 | 20200413152932.0 | ||
006 | m eo d | ||
007 | cr bn |||m|||a | ||
008 | 190503s2019 caua fob 001 0 eng d | ||
020 |
_a9781681735641 _qelectronic |
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020 |
_z9781681735658 _qhardcover |
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020 |
_z9781681735634 _qpaperback |
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024 | 7 |
_a10.2200/S00917ED1V04Y201904MAS026 _2doi |
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035 | _a(CaBNVSL)thg00978847 | ||
035 | _a(OCoLC)1099982222 | ||
040 |
_aCaBNVSL _beng _erda _cCaBNVSL _dCaBNVSL |
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050 | 4 |
_aQA641 _b.C252 2019eb |
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082 | 0 | 4 |
_a516.36 _223 |
100 | 1 |
_aCalviño-Louzao, Esteban, _eauthor. |
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245 | 1 | 0 |
_aAspects of differential geometry IV / _cEsteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo. |
264 | 1 |
_a[San Rafael, California] : _bMorgan & Claypool, _c[2019] |
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300 |
_a1 PDF (xvii, 149 pages) : _billustrations (some color). |
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336 |
_atext _2rdacontent |
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337 |
_aelectronic _2isbdmedia |
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338 |
_aonline resource _2rdacarrier |
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490 | 1 |
_aSynthesis lectures on mathematics and statistics, _x1938-1751 ; _v#26 |
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538 | _aMode of access: World Wide Web. | ||
538 | _aSystem requirements: Adobe Acrobat Reader. | ||
500 | _aPart of: Synthesis digital library of engineering and computer science. | ||
504 | _aIncludes bibliographical references (pages 137-141) and index. | ||
505 | 0 | _a12. An introduction to affine geometry -- 12.1. Basic definitions -- 12.2. Surfaces with recurrent Ricci tensor -- 12.3. The affine quasi-Einstein equation -- 12.4. The classification of locally homogeneous affine surfaces with torsion -- 12.5. Analytic structure for homogeneous affine surfaces | |
505 | 8 | _a13. The geometry of type A models -- 13.1. Type A : foundational results and basic examples -- 13.2. Type A : distinguished geometries -- 13.3. Type A : parameterization -- 13.4. Type A : moduli spaces | |
505 | 8 | _a14. The geometry of type B models -- 14.1. Type B : distinguished geometries -- 14.2. Type B : affine killing vector fields -- 14.3. Symmetric spaces | |
505 | 8 | _a15. Applications of affine surface theory -- 15.1. Preliminary matters -- 15.2. Signature (2, 2) VSI manifolds -- 15.3. Signature (2, 2) bach flat manifolds. | |
506 | _aAbstract freely available; full-text restricted to subscribers or individual document purchasers. | ||
510 | 0 | _aCompendex | |
510 | 0 | _aINSPEC | |
510 | 0 | _aGoogle scholar | |
510 | 0 | _aGoogle book search | |
520 | 3 | _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 ax + b group is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type A surfaces. These are the left-invariant affine geometries on R2. Associating to each Type A surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue [mu] = -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 B surfaces; these are the left-invariant affine geometries on the ax + b group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere S2. 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. | |
530 | _aAlso available in print. | ||
588 | _aTitle from PDF title page (viewed on May 3, 2019). | ||
650 | 0 | _aGeometry, Differential. | |
653 | _aaffine gradient Ricci solitons | ||
653 | _aaffine Killing vector fields | ||
653 | _ageodesic completeness | ||
653 | _alocally homogeneous affine surfaces | ||
653 | _alocally symmetric affine surfaces | ||
653 | _aprojectively flat | ||
653 | _aquasi-Einstein equation | ||
700 | 1 |
_aGarcía-Río, Eduardo, _eauthor. |
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700 | 1 |
_aGilkey, Peter B., _eauthor. |
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700 | 1 |
_aPark, Jeonghyeong, _eauthor. |
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700 | 1 |
_aVázquez-Lorenzo, Ramón, _eauthor |
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776 | 0 | 8 |
_iPrint version: _z9781681735658 _z9781681735634 |
830 | 0 | _aSynthesis digital library of engineering and computer science. | |
830 | 0 |
_aSynthesis lectures on mathematics and statistics ; _v#26. |
|
856 | 4 | 0 |
_3Abstract with links to full text _uhttps://doi.org/10.2200/S00917ED1V04Y201904MAS026 |
856 | 4 | 2 |
_3Abstract with links to resource _uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=8694982 |
999 |
_c562407 _d562407 |