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Aspects of differential geometry IV /

Calviño-Louzao, Esteban,

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Aspects of differential geometry IV /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Aspects of differential geometry IV // Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo.
Author:	Calviño-Louzao, Esteban,
other author:	García-Río, Eduardo,
Description:	1 online resource (169 p.)
[NT 15003449]:	Aspects of differential geometry IV -- Contents -- Preface -- Acknowledgments -- Chapter 12. An Introduction to Affine Geometry -- Chapter 13. The Geometry of Type A Models -- Chapter 14. The Geometry of Type B Models -- Chapter 15. Applications of Affine Surface Theory -- Bibliography -- Authors' Biographies -- Index.
Subject:	Geometry, Differential. -
Online resource:	https://portal.igpublish.com/iglibrary/search/MCPB0006468.html
ISBN:	9781681735634

Aspects of differential geometry IV /
Calviño-Louzao, Esteban,

Aspects of differential geometry IV /Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo. - 1st ed. - 1 online resource (169 p.) - Synthesis lectures on mathematics and statistics. - Synthesis lectures on mathematics and statistics..

Includes bibliographical references and index.

Aspects of differential geometry IV -- Contents -- Preface -- Acknowledgments -- Chapter 12. An Introduction to Affine Geometry -- Chapter 13. The Geometry of Type A Models -- Chapter 14. The Geometry of Type B Models -- Chapter 15. Applications of Affine Surface Theory -- Bibliography -- Authors' Biographies -- Index.

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: 9781681735634Subjects--Topical Terms:

523835
Geometry, Differential.
Index Terms--Genre/Form:

542853
Electronic books.

LC Class. No.: QA641

Dewey Class. No.: 516.3/6

Aspects of differential geometry IV /
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245 1 0 $a Aspects of differential geometry IV / $c Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo.
250 $a 1st ed.
264 1 $a [San Rafael, California] : $b Morgan & Claypool Publishers, $c 2019.
300 $a 1 online resource (169 p.)
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505 0 $a Aspects of differential geometry IV -- Contents -- Preface -- Acknowledgments -- Chapter 12. An Introduction to Affine Geometry -- Chapter 13. The Geometry of Type A Models -- Chapter 14. The Geometry of Type B Models -- Chapter 15. Applications of Affine Surface Theory -- Bibliography -- Authors' Biographies -- Index.
520 $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.
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655 4 $a Electronic books. $2 lcsh $3 542853
700 1 $a García-Río, Eduardo, $e author. $3 3440552
700 1 $a Gilkey, Peter, $e author. $3 3440553
700 1 $a Park, JeongHyeong, $e author. $3 3440554
700 1 $a Vázquez-Lorenzo, Ramón, $e author. $3 3440555
830 0 $a Synthesis lectures on mathematics and statistics. $3 3440556
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