Geometric realizations of curvature
 Responsibility
 Miguel Brozos Vázquez, Peter B Gilkey, Stana Nikcevic.
 Language
 English.
 Imprint
 London, England : Imperial College Press, c2012.
 Physical description
 ix, 252 p. ; 24 cm.
 Series
 Imperial College Press advanced texts in mathematics ; v. 6.
Access
Available online
 www.worldscientific.com World Scientific
 ebrary
Math & Statistics Library

Stacks

Unknown
QA360 .B76 2012

Unknown
QA360 .B76 2012
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Creators/Contributors
 Author/Creator
 BrozosVázquez, Miguel.
 Contributor
 Gilkey, Peter B.
 Nikcevic, Stana.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 239247) and index.
 Contents

 Introduction and Statement of Results Representation Theory Connections, Curvature, and Differential Geometry Affine Geometry Kahler and ParaKahler Geometry Affine Geometry Riemannian Geometry Complex and ParaComplex Geometry Hyper Complex Geometry and Other Questions.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 SingerThorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the TricerriVanhecke decomposition, the GrayHervella 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 pseudoRiemannian setting and then further, in a complex framework, to paraHermitian 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Geometric analysis.
Bibliographic information
 Publication date
 2012
 Series
 ICP advanced texts in mathematics, 1753657X ; v. 6
 ISBN
 9781848167414
 1848167415