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arXiv · 0901.1633

The geometry of modified Riemannian extensions

E. Calvino-Louzao·E. Garcia-Rio·P. Gilkey·R. Vazquez-Lorenzo
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Abstract

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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E. Calvino-Louzao, E. Garcia-Rio, P. Gilkey, R. Vazquez-Lorenzo. 2009-01-12. The geometry of modified Riemannian extensions. https://doi.org/10.1098/rspa.2009.0046

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