Symplectic Connections Induced by the Chern Connection

Ebrahim Esrafilian; Hamid Reza Salimi Moghaddam

Symplectic Connections Induced by the Chern Connection

Differential Geometry 2015-07-09 v1

Authors: Ebrahim Esrafilian , Hamid Reza Salimi Moghaddam

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 $M$ .

Keywords

symplectic manifold Finsler structure Chern connection symplectic two-form Fedosov structure nowhere zero vector field

Cite

@article{arxiv.1305.2852,
  title  = {Symplectic Connections Induced by the Chern Connection},
  author = {Ebrahim Esrafilian and Hamid Reza Salimi Moghaddam},
  journal= {arXiv preprint arXiv:1305.2852},
  year   = {2015}
}

Symplectic Connections Induced by the Chern Connection

Abstract

Keywords

Cite

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