The geometry of modified Riemannian extensions

By E. Calviño-Louzao, E. García‐Río, P. Gilkey, Ramón Vázquez-Lorenzo. Proceedings of the Royal Society A, 2009

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We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be 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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

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