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arXiv · 1305.2852

Symplectic Connections Induced by the Chern Connection

Ebrahim Esrafilian·Hamid Reza Salimi Moghaddam
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Abstract

Let $(M,\omega)$ be a symplectic manifold and $F$ be a Finsler structure on $M$. In the present paper we define a lift of the symplectic two-form $\omega$ on the manifold $TM\backslash 0$, and find the conditions that the Chern connection of the Finsler structure $F$ preserves this lift of $\omega$. In this situation if $M$ admits a nowhere zero vector field then we have a non-empty family of Fedosov structures on $M$.

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Ebrahim Esrafilian, Hamid Reza Salimi Moghaddam. 2013-05-01. Symplectic Connections Induced by the Chern Connection. https://arxiv.org/abs/1305.2852

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