Puffini-Videv Models and Manifolds

2006/05/17 by Peter Gilkey, Gilkey, P., E. Puffini +3
Mathematics · #53C20 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0605464

openalex publication_date 2006/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let J(π) be the higher order Jacobi operator. We study algebraic curvature tensors where J(π)J(π^⊥)=J(π^⊥)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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