Higher order Jordan Osserman Pseudo-Riemannian manifolds
Differential Geometry
2009-11-07 v2 Mathematical Physics
math.MP
Abstract
We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r,s) for certain values of (r,s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher order Osserman manifolds.
Cite
@article{arxiv.math/0205269,
title = {Higher order Jordan Osserman Pseudo-Riemannian manifolds},
author = {Peter B. Gilkey and Raina Ivanova and Tan Zhang},
journal= {arXiv preprint arXiv:math/0205269},
year = {2009}
}