Puffini-Videv Models and Manifolds

Abstract

Let $J(\pi )$ be the higher order Jacobi operator. We study algebraic curvature tensors where $J(\pi )J({\pi }^{\perp })=J({\pi }^{\perp })J(\pi )$. In the Riemannian setting, we give a complete characterization of such tensors; in the pseudo-Riemannian setting, partial results are available. We present non-trivial geometric examples of Riemannian manifolds with this property.

6 pages

Cited by in corpus (2)

• Stanilov-Tsankov-Videv Theory
• Four-dimensional Riemannian manifolds with commuting higher order Jacobi operators