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Geometric realizations of curvature

Brozos-Vázquez, Miguel.

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Geometric realizations of curvature

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric realizations of curvature/ Miguel Brozos Vázquez, Peter B. Gilkey, Stana Nikcevic.
Author:	Brozos-Vázquez, Miguel.
other author:	Gilkey, Peter B.
Published:	London :Imperial College Press, : 2012.,
Description:	1 online resource (ix, 252 p.) :ill.
Subject:	Curvature. -
Online resource:	http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc
ISBN:	9781848167421 (electronic bk.)

Geometric realizations of curvature
Brozos-Vázquez, Miguel.

Geometric realizations of curvature[electronic resource] /Miguel Brozos Vázquez, Peter B. Gilkey, Stana Nikcevic. - London :Imperial College Press,2012. - 1 online resource (ix, 252 p.) :ill. - ICP advanced texts in mathematics,v. 61753-657X ;. - Imperial College Press advanced texts in mathematics ;v. 6..

Includes bibliographical references and index.

A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature.

ISBN: 9781848167421 (electronic bk.)Subjects--Topical Terms:

711378
Curvature.
Index Terms--Genre/Form:

542853
Electronic books.

LC Class. No.: QA645 / .V39 2012eb

Dewey Class. No.: 515/.1

Geometric realizations of curvature
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520 $a A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature.
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