Pseudo-Riemannian Jacobi-Videv Manifolds

TL;DR

This paper introduces new examples of pseudo-Riemannian manifolds and algebraic curvature tensors that are Jacobi-Videv but not Einstein, highlighting diverse geometric structures with special curvature properties.

Contribution

It presents novel families of Jacobi-Videv pseudo-Riemannian manifolds and algebraic curvature tensors with Ricci operators forming almost complex structures, expanding understanding of curvature conditions.

Findings

Several families of Jacobi-Videv pseudo-Riemannian manifolds not Einstein.

Jacobi-Videv algebraic curvature tensors with Ricci operators as almost complex structures.

New examples illustrating the diversity of Jacobi-Videv geometries.

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.