The geometry of modified Riemannian extensions

We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-...

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Bibliographic Details
Published in:	Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 465; no. 2107; pp. 2023 - 2040
Main Authors:	E. Calviño-Louzao, E. García-Río, P. Gilkey, R. Vázquez-Lorenzo
Format:	Journal Article
Language:	English
Published:	London The Royal Society 08-07-2009
Subjects:	Affine Connection Coordinate systems Curvature Eigenvalues Einstein Geometry Jacobi Operator Mathematical theorems Modified Riemannian Extension Osserman Manifold Para-Kaehler Riemann manifold Signatures Symmetry Tensors
Online Access:	Get full text
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Summary:	We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent. We present new four-dimensional results in Osserman geometry.
Bibliography:	href:2023.pdf istex:A3DFBC0184DEFECE12A67774132243C60A4C4134 ark:/67375/V84-RVDXKXZ1-H ArticleID:rspa20090046
ISSN:	1364-5021 1471-2946
DOI:	10.1098/rspa.2009.0046