Remarks on special symplectic connections

TL;DR

This paper revisits special symplectic connections, offering a more explicit construction method by pulling back ambient linear connections from scale bundles over contact parabolic geometries, expanding understanding of their structure.

Contribution

It provides an alternative, explicit construction of three types of special symplectic connections using ambient linear connections and scale bundles, building on previous characterizations.

Findings

Explicit construction method for special symplectic connections

Connection to contact parabolic geometries clarified

Generalized Weyl connections used in reinterpretation

Abstract

The notion of special symplectic connections is closely related to contact parabolic geometries due to the work of M. Cahen and L. Schwachh\"ofer. 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 contact parabolic structure.