Symplectic structures preserved by geodesic symmetries
Symplectic Geometry
2025-08-27 v2
Abstract
Answering a conjecture by S. Kobayashi, in 1986, K. Sekigawa and L. Vanhecke proved that an almost hermitian manifold whose local geodesic symmetries preserve the K\"ahler 2-form is a locally symmetric hermitian space. In the present paper, we relax the hermitean hypothesis by only requiring the manifold to be symplectic. In other words, we study the symplectic manifolds equipped with a symplectic connection whose geodesic symmetries are (local) symplectomorphisms. We call ``S-type'' these affine symplectic manifolds.
Cite
@article{arxiv.2411.05702,
title = {Symplectic structures preserved by geodesic symmetries},
author = {Pierre Bieliavsky and Maxime Willaert},
journal= {arXiv preprint arXiv:2411.05702},
year = {2025}
}