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Aspects of differential geometry IV /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Aspects of differential geometry IV // Esteban Calvi�no-Louzao, Eduardo Garc�ia-R�io, Peter Gilkey, JeongHyeong Park, Ram�on V�azquez-Lorenzo.
Author:	Calvi�no-Louzao, Esteban,
other author:	Garc�ia-R�io, Eduardo,
Description:	1 PDF (xvii, 149 pages) :illustrations (some color). :
Notes:	Part of: Synthesis digital library of engineering and computer science.
Subject:	Geometry, Differential. -
Online resource:	https://doi.org/10.2200/S00917ED1V04Y201904MAS026
Online resource:	https://ieeexplore.ieee.org/servlet/opac?bknumber=8694982
ISBN:	9781681735641

Aspects of differential geometry IV /
Calvi�no-Louzao, Esteban,

Aspects of differential geometry IV /Esteban Calvi�no-Louzao, Eduardo Garc�ia-R�io, Peter Gilkey, JeongHyeong Park, Ram�on V�azquez-Lorenzo. - 1 PDF (xvii, 149 pages) :illustrations (some color). - Synthesis lectures on mathematics and statistics,#261938-1751 ;. - Synthesis digital library of engineering and computer science..

Part of: Synthesis digital library of engineering and computer science.

Includes bibliographical references (pages 137-141) and index.

12. 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

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

Compendex

Book 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.

Mode of access: World Wide Web.

ISBN: 9781681735641

Standard No.: 10.2200/S00917ED1V04Y201904MAS026doiSubjects--Topical Terms:

527830
Geometry, Differential.
Subjects--Index Terms:

affine gradient Ricci solitons

LC Class. No.: QA641 / .C252 2019eb

Dewey Class. No.: 516.36

Aspects of differential geometry IV /
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100 1 $a Calvi�no-Louzao, Esteban, $e author. $3 1253093
245 1 0 $a Aspects of differential geometry IV / $c Esteban Calvi�no-Louzao, Eduardo Garc�ia-R�io, Peter Gilkey, JeongHyeong Park, Ram�on V�azquez-Lorenzo.
264 1 $a [San Rafael, California] : $b Morgan & Claypool, $c [2019]
300 $a 1 PDF (xvii, 149 pages) : $b illustrations (some color).
336 $a text $2 rdacontent
337 $a electronic $2 isbdmedia
338 $a online resource $2 rdacarrier
490 1 $a Synthesis lectures on mathematics and statistics, $x 1938-1751 ; $v #26
500 $a Part of: Synthesis digital library of engineering and computer science.
504 $a Includes bibliographical references (pages 137-141) and index.
505 0 $a 12. 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 $a 13. 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 $a 14. 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 $a 15. 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 $a Abstract freely available; full-text restricted to subscribers or individual document purchasers.
510 0 $a Compendex
510 0 $a INSPEC
510 0 $a Google scholar
510 0 $a Google book search
520 3 $a Book 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 $a Also available in print.
538 $a Mode of access: World Wide Web.
538 $a System requirements: Adobe Acrobat Reader.
588 $a Title from PDF title page (viewed on May 3, 2019).
650 0 $a Geometry, Differential. $3 527830
653 $a affine gradient Ricci solitons
653 $a affine Killing vector fields
653 $a geodesic completeness
653 $a locally homogeneous affine surfaces
653 $a locally symmetric affine surfaces
653 $a projectively flat
653 $a quasi-Einstein equation
700 1 $a Garc�ia-R�io, Eduardo, $e author. $3 1253094
700 1 $a Gilkey, Peter B., $e author. $3 1253095
700 1 $a Park, Jeonghyeong, $e author. $3 1253096
700 1 $a V�azquez-Lorenzo, Ram�on, $e author $3 1253097
776 0 8 $i Print version: $z 9781681735658 $z 9781681735634
830 0 $a Synthesis digital library of engineering and computer science. $3 598254
830 0 $a Synthesis lectures on mathematics and statistics ; $v #26. $3 1253098
856 4 0 $3 Abstract with links to full text $u https://doi.org/10.2200/S00917ED1V04Y201904MAS026
856 4 2 $3 Abstract with links to resource $u https://ieeexplore.ieee.org/servlet/opac?bknumber=8694982