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The geometry of modified Riemannian extensions. (English) Zbl 1186.53056

Summary: 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.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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