Puffini-Videv Models and Manifolds

Gilkey, P.; Puffini, E.; Videv, V.

Puffini-Videv Models and Manifolds

Authors

Gilkey, P.

Puffini, E.

Videv, V.

Description

Let $J(π)$ be the higher order Jacobi operator. We study algebraic curvature tensors where $J(π)J(π^{\perp})=J(π^{\perp})J(π)$. 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