The geometry of modified Riemannian extensions

E. Calvino-Louzao, E. Garcia-Rio, P. Gilkey, R. Vazquez-Lorenzo
2009 Proceedings of the Royal Society A  
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.
doi:10.1098/rspa.2009.0046 fatcat:aec2utbxfrep5kphgirgbi2kb4