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

2002/06/08 by Novica Blažić, Novica Blazic, Blazic, Novica +3
Mathematics · Physics and Astronomy · #53C07 #53C15 #53C80 #53G10 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53C07 #msc:53C15 #msc:53C80 #msc:53G10

paper · pdf · doi:10.48550/arxiv.math/0206081

9 pages, LaTex2e

arxiv created 2002/06/08 · openalex publication_date 2002/06/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \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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