Puffini-Videv Models and Manifolds

arXivmath/0605464MaRDI QIDQ6477218

Veselin T. Videv, E. Puffini, Peter B. Gilkey

Publication date: 17 May 2006

Abstract: Let $J(pi)$ be the higher order Jacobi operator. We study algebraic curvature tensors where $J(pi)J(p{i}^{perp})=J(p{i}^{perp})J(pi)$. 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.

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

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