Complete k-curvature homogeneous pseudo-Riemannian manifolds
Differential Geometry
2007-05-23 v1
Abstract
For any k which is at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not k+1-affine curvature homogeneous, and hence not locally homogeneous. All the local scalar Weyl invariants of these manifolds vanish. These manifolds are Ricci flat, Osserman, and Ivanov-Petrova.
Cite
@article{arxiv.math/0405024,
title = {Complete k-curvature homogeneous pseudo-Riemannian manifolds},
author = {P. Gilkey and S. Nikcevic},
journal= {arXiv preprint arXiv:math/0405024},
year = {2007}
}