On quasi-Clifford Osserman curvature tensors

TL;DR

This paper introduces quasi-Clifford curvature tensors in pseudo-Riemannian geometry, demonstrating they are Osserman and exploring their relation to the duality principle, including conditions for its validity.

Contribution

It defines quasi-Clifford curvature tensors using generalized Clifford families and shows they are Osserman, revealing new examples that challenge existing duality principle assumptions.

Findings

Quasi-Clifford tensors are Osserman.

An Osserman tensor can violate the duality principle.

Conditions for the total duality principle are provided.

Abstract

We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the duality principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi-Clifford curvature tensors using a generalized Clifford family and show that they are Osserman. This allows us to discover an Osserman curvature tensor that does not satisfy the duality principle. We give some necessary and some sufficient conditions for the total duality principle.