Riemannian manifolds of dimension 7 whose skew-symmetric curvature operator has constant eigenvalues
Differential Geometry
2007-05-23 v2
Abstract
A Riemannian manifold is called IP, if the eigenvalues of its skew-symmetric curvature operator are pointwise constant. It was previously shown that for all n\ge 4, except n=7, any IP manifold either has constant curvature, or is a warped product, with some specific function, of a line and a space of constant curvature. We extend this result to the case n = 7, and also study 3-dimensional IP manifolds.
Keywords
Cite
@article{arxiv.math/0311429,
title = {Riemannian manifolds of dimension 7 whose skew-symmetric curvature operator has constant eigenvalues},
author = {Y. Nikolayevsky},
journal= {arXiv preprint arXiv:math/0311429},
year = {2007}
}
Comments
Corollary on p2 corrected