Symplectic structures preserved by geodesic symmetries

Pierre Bieliavsky; Maxime Willaert

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arXiv · 2411.05702

Symplectic structures preserved by geodesic symmetries

Pierre Bieliavsky·Maxime Willaert

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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.

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BibTeX RIS

Pierre Bieliavsky, Maxime Willaert. 2024-11-08. Symplectic structures preserved by geodesic symmetries. https://arxiv.org/abs/2411.05702

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