Examples of pointwise Osserman manifolds of neutral signature

Abstract

This is an overview of the paper [1], a joint work with Novica Blažić. Let p, q be relatively prime natural numbers. We consider certain isometric action ϕp,q t of an one-dimensional non-compact Lie group on the paraquaternionic projective plane ¯HP 2 of signature (4, 4). This action preserves the paraquaternionic structure on the projective plane. By the method of paraquaternionic reduction, a family of orbifolds Op,q with an induced metric of signature (2,2) is obtained. We study the eometry of these orbifolds. In particular, we show that the orbifolds Op,q are pointwise Osserman, but not even locally homogeneous.