Examples of Self-dual, Einstein metrics of $(2,2)$-signature

Details Examples of Self-dual, Einstein metrics of $(2,2)$-signature Examples of Self-dual, Einstein metrics of $(2,2)$-signature

2002-06-08

arxiv.org/abs/math/0206081v1

Mathematics

Differential Geometry

9 pages, LaTex2e

Scientific paper

In this paper we construct a family of examples of self-dual Einstain metrics of neutral signature, which are not Ricci flat, nor locally homogenous. Curvature of these manifolds is studied in details. These are obtained by the para-quaternionic reduction. We compare our examples with the orbifolds $\oo$ given by Galicki and Lawson, for which some new properties are also established. Particularly, the sign and the pinching of their sectional curvatures are studied.

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