The Duality principle for Osserman algebraic curvature tensors

TL;DR

This paper establishes a connection between the Jordan-Osserman condition and the Rakić duality principle for algebraic curvature tensors, showing their equivalence under certain conditions in pseudo-Euclidean spaces.

Contribution

It proves that the Jordan-Osserman condition implies the Rakić duality principle and that they are equivalent for diagonalisable algebraic curvature tensors.

Findings

Jordan-Osserman condition implies Rakić duality principle

Osserman condition and duality principle are equivalent in diagonalisable case

Results apply to algebraic curvature tensors on pseudo-Euclidean spaces

Abstract

We prove that for an algebraic curvature tensor on a pseudo-Euclidean space, the Jordan-Osserman condition implies the Raki\'c duality principle, and that the Osserman condition and the duality principle are equivalent in the diagonalisable case.