Remarks on Special Symplectic Connections

Martin Panák and Vojtěch Žádník

Address: Department of Mathematics and Statistics Masaryk University 611 37 Brno, Czech Republic


Abstract: The notion of special symplectic connections is closely related to parabolic contact geometries due to the work of M. Cahen and L. Schwachhöfer. We remind their characterization and reinterpret the result in terms of generalized Weyl connections. The aim of this paper is to provide an alternative and more explicit construction of special symplectic connections of three types from the list. This is done by pulling back an ambient linear connection from the total space of a natural scale bundle over the homogeneous model of the corresponding parabolic contact structure.

AMSclassification: primary 53D15; secondary 53C15, 53B15.

Keywords: special symplectic connections, parabolic contact geometries, Weyl structures and connections.