Puffini-Videv Models and Manifolds

Details Puffini-Videv Models and Manifolds Puffini-Videv Models and Manifolds

2006-05-17

arxiv.org/abs/math/0605464v1

Mathematics

Differential Geometry

6 pages

Scientific paper

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.

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