The classification of simple Jacobi--Ricci commuting algebraic curvature tensors

P. Gilkey; S. Nikcevic

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arXiv · 0710.2080

The classification of simple Jacobi--Ricci commuting algebraic curvature tensors

P. Gilkey·S. Nikcevic

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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).

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P. Gilkey, S. Nikcevic. 2007-10-10. The classification of simple Jacobi--Ricci commuting algebraic curvature tensors. https://arxiv.org/abs/0710.2080

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