The geometry of modified Riemannian extensions

Details The geometry of modified Riemannian extensions The geometry of modified Riemannian extensions

2009-01-12

arxiv.org/abs/0901.1633v1

Mathematics

Differential Geometry

Scientific paper

We show that every paracomplex space form is locally isometric to a modified Riemannian extension and give necessary and sufficient conditions so that a modified Riemannian extension is Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3,3) whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent. We present new four dimensional results in Osserman geometry.

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