English

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 JXYJYX\mathcal{J}_XY\perp\mathcal{J}_YX holds for all XYX\perp Y, where J\mathcal{J} 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}
}
R2 v1 2026-06-28T12:06:38.954Z