A01=Miguel Brozos-vazquez
A01=Peter B Gilkey
A01=Stana Z Nikcevic
Affine Geometry
Almost Complex Geometry
Author_Miguel Brozos-vazquez
Author_Peter B Gilkey
Author_Stana Z Nikcevic
Category=PBMP
Curvature Decompositions
Curvature Tensor
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Hermitian Geometry
Hyper-Hermitian Geometry
KAfA?hler Geometry
Kahler Geometry
Kähler Geometry
Para-Hermitian Geometry
Para-KAfA?hler Geometry
Para-Kahler Geometry
Para-Kähler Geometry
Pseudo-Riemannian Geometry
Riemannian Geometry
Weyl Geometry
Product details
- ISBN 9781848167414
- Publication Date: 19 Mar 2012
- Publisher: Imperial College Press
- Publication City/Country: GB
- Product Form: Hardback
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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.
