The classification of simple Jacobi--Ricci commuting algebraic curvature tensors
Differential Geometry
2007-10-11 v1
Abstract
We classify algebraic curvature tensors such that the Ricci operator is simple (i.e. the Ricci operator is complex diagonalizable and either the complex spectrum consists of a single real eigenvalue or the complex spectrum consists of a pair of eigenvalues which are complex conjugates of each other) and which are Jacobi--Ricci commuting (i.e. the Ricci operator commutes with the Jacobi operator of any vector).
Keywords
Cite
@article{arxiv.0710.2080,
title = {The classification of simple Jacobi--Ricci commuting algebraic curvature tensors},
author = {P. Gilkey and S. Nikcevic},
journal= {arXiv preprint arXiv:0710.2080},
year = {2007}
}