Pseudo-Riemannian Jacobi-Videv Manifolds

Abstract

We exhibit several families of Jacobi-Videv pseudo-Riemannian manifolds which are not Einstein. We also exhibit Jacobi-Videv algebraic curvature tensors where the Ricci operator defines an almost complex structure.

References in corpus (2)

• Completeness, Ricci blowup, the Osserman and the conformal Osserman condition for Walker signature (2,2) manifolds
• Four-dimensional Riemannian manifolds with commuting higher order Jacobi operators

Cited by in corpus (7)

• Stanilov-Tsankov-Videv Theory
• Examples of signature (2,2) manifolds with commuting curvature operators
• Geometric realizations of Kaehler and of para-Kaehler curvature models
• Curvature structure of self-dual 4-manifolds
• Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
• Geometric Realizations of Hermitian curvature models
• The classification of simple Jacobi--Ricci commuting algebraic curvature tensors