Commentarii Mathematici Helvetici


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Volume 77, Issue 2, 2002, pp. 383–398
DOI: 10.1007/s00014-002-8345-z

Published online: 2002-06-30

Some properties of locally conformal symplectic structures

A. Banyaga[1]

(1) The Pennsylvania State University, University Park, USA

We show that the $ d_{\omega} $-cohomology is isomorphic to a conformally invariant usual de Rham cohomology of an appropriate cover. We also prove a Moser theorem for locally conformal symplectic (lcs) forms. We point out a connection between lcs geometry and contact geometry. Finally, we show the connections between first kind, second kind, essential, inessential, local, and global conformal symplectic structures through several invariants.

Keywords: Locally conformal symplectic structures, Lee form, extended Lee homomorphism, de Rham invariant, Gelfand-Fucks invariant, Lee invariant, conformal invariants, essential / inessential conformal structures, the $ d_{\omega} $ cohomology, the $ c\mathcal{A}

Banyaga A.: Some properties of locally conformal symplectic structures. Comment. Math. Helv. 77 (2002), 383-398. doi: 10.1007/s00014-002-8345-z