The Orthogonality Principle for Osserman Manifolds
Differential Geometry
2023-08-30 v1
Abstract
We introduce a new potential characterization of Osserman algebraic curvature tensors. An algebraic curvature tensor is Jacobi-orthogonal if holds for all , where denotes the Jacobi operator. We prove that any Jacobi-orthogonal tensor is Osserman, while all known Osserman tensors are Jacobi-orthogonal.
Keywords
Cite
@article{arxiv.2308.14851,
title = {The Orthogonality Principle for Osserman Manifolds},
author = {Vladica Andrejić and Katarina Lukić},
journal= {arXiv preprint arXiv:2308.14851},
year = {2023}
}