Extrinsic symplectic symmetric spaces

TL;DR

This paper introduces extrinsic symplectic symmetric spaces, explores their properties, constructs numerous examples, and develops a star-quantization method for some of these manifolds.

Contribution

It defines extrinsic symplectic symmetric spaces, provides a classification framework, and introduces a star-quantization approach for specific cases.

Findings

Construction of large families of extrinsic symplectic symmetric spaces

Properties and classification of these spaces

Development of a star-quantization method for certain examples

Abstract

We define the notion of extrinsic symplectic symmetric spaces and exhibit some of their properties. We construct large families of examples and show how they fit in the perspective of a complete classification of these manifolds. We also build a natural star-quantization on a class of examples.