A note on Raki\'c duality principle for Osserman manifolds

TL;DR

This paper establishes that for Riemannian manifolds, the Osserman condition at a point is equivalent to satisfying the Rakić duality principle, linking two important geometric properties.

Contribution

It proves the equivalence between the Osserman condition and the Rakić duality principle for Riemannian manifolds, clarifying their relationship.

Findings

Osserman condition is equivalent to Rakić duality for Riemannian manifolds

Provides a new perspective on the geometric properties of manifolds

Simplifies the analysis of Osserman manifolds by using duality principles

Abstract

In this note we prove that for a Riemannian manifold the Osserman pointwise condition is equivalent to the Raki\'c duality principle.