Puffini-Videv Models and Manifolds

P. Gilkey; E. Puffini; V. Videv

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arXiv · math/0605464

Puffini-Videv Models and Manifolds

P. Gilkey·E. Puffini·V. Videv

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Abstract

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.

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BibTeX RIS

P. Gilkey, E. Puffini, V. Videv. 2006-05-17. Puffini-Videv Models and Manifolds. https://arxiv.org/abs/math/0605464

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