English

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}
}
R2 v1 2026-06-21T11:59:55.207Z