000 05267nam a2200709 i 4500
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
020 _z9781681735658
_qhardcover
020 _z9781681735634
_qpaperback
024 7 _a10.2200/S00917ED1V04Y201904MAS026
_2doi
035 _a(CaBNVSL)thg00978847
035 _a(OCoLC)1099982222
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQA641
_b.C252 2019eb
082 0 4 _a516.36
_223
100 1 _aCalviño-Louzao, Esteban,
_eauthor.
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]
300 _a1 PDF (xvii, 149 pages) :
_billustrations (some color).
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _aSynthesis lectures on mathematics and statistics,
_x1938-1751 ;
_v#26
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.
700 1 _aGilkey, Peter B.,
_eauthor.
700 1 _aPark, Jeonghyeong,
_eauthor.
700 1 _aVázquez-Lorenzo, Ramón,
_eauthor
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