The geometry of modified Riemannian extensions

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Calvino-Louzao, E.
Garcia-Rio, E.
Gilkey, P.
Vazquez-Lorenzo, R.
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Abstract
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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.
Keywords
Mathematics - Differential Geometry, 53C50, 53B30
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