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