The geometry of modified Riemannian extensions
Differential Geometry
2015-05-13 v1
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.
Keywords
Cite
@article{arxiv.0901.1633,
title = {The geometry of modified Riemannian extensions},
author = {E. Calvino-Louzao and E. Garcia-Rio and P. Gilkey and R. Vazquez-Lorenzo},
journal= {arXiv preprint arXiv:0901.1633},
year = {2015}
}