Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2

Peter Gilkey; Tan Zhang

Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2

Differential Geometry 2007-05-23 v1

Authors: Peter Gilkey , Tan Zhang

Abstract

Let R be an algebraic curvature tensor for a non-degenerate inner product of signature(p,q) where q>4. If $\pi$ is a spacelike 2 plane, let $R(\pi)$ be the associated skew-symmetric curvature operator. We classify the algebraic curvature tensors so R(-) has constant rank 2 and show these are geometrically realizable by hypersurfaces in flat spaces. We also classify the Ivanov-Petrova algebraic curvature tensors of rank 2; these are the algebraic curvature tensors of constant rank 2 such that the complex Jordan normal form of R(-) is constant.

Keywords

algebraic curvature tensor skew-symmetric curvature operator constant rank ivanov-petrova hypersurfaces

Cite

@article{arxiv.math/0205080,
  title  = {Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2},
  author = {Peter Gilkey and Tan Zhang},
  journal= {arXiv preprint arXiv:math/0205080},
  year   = {2007}
}

Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2

Abstract

Keywords

Cite

Related papers