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

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

2007-10-10

arxiv.org/abs/0710.2080v1

Mathematics

Differential Geometry

Scientific paper

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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