Curvature-homogeneous indefinite Einstein metrics in dimension four: the diagonalizable case

Details Curvature-homogeneous indefinite Einstein metrics in dimension four: the diagonalizable case Curvature-homogeneous indefinite Einstein metrics in dimension four: the diagonalizable case

2002-11-16

arxiv.org/abs/math/0211248v1

Contemporary Mathematics, vol. 337, American Mathematical Society, Providence, RI, 2003, pp. 21-38

Mathematics

Differential Geometry

AMS-TeX 2.1, 18 pages, no figures, submitted to an AMS volume of Proceedings in Contemporary Mathematics

Scientific paper

We classify those curvature-homogeneous Einstein four-manifolds, of all metric signatures, which have a complex-diagonalizable curvature operator. They all turn out to be locally homogeneous. More precisely, any such manifold must be either locally symmetric or locally isometric to a suitable Lie group with a left-invariant metric. To show this we explicitly determine the possible local-isometry types of manifolds that have the properties named above, but are not locally symmetric.

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