Algebraic curvature tensors for indefinite metrics whose skew-symmetric curvature operator has constant Jordan normal form

Peter Gilkey; Tan Zhang

Algebraic curvature tensors for indefinite metrics whose skew-symmetric curvature operator has constant Jordan normal form

Differential Geometry 2007-05-23 v1

Authors: Peter Gilkey , Tan Zhang

Abstract

We classify the connected pseudo-Riemannian manifolds of signature $(p,q)$ with $q\ge5$ so that at each point of $M$ the skew-symmetric curvature operator has constant rank 2 and constant Jordan normal form on the set of spacelike 2 planes and so that the skew-symmetric curvature operator is not nilpotent for at least one point of $M$ .

Keywords

pseudo-riemannian manifold algebraic curvature tensor skew-symmetric curvature operator jordan normal form constant rank

Cite

@article{arxiv.math/0205079,
  title  = {Algebraic curvature tensors for indefinite metrics whose skew-symmetric curvature operator has constant Jordan normal form},
  author = {Peter Gilkey and Tan Zhang},
  journal= {arXiv preprint arXiv:math/0205079},
  year   = {2007}
}

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