English

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