Fedosov supermanifolds: II. Normal coordinates

TL;DR

This paper extends the study of Fedosov supermanifolds by analyzing their properties in normal coordinates, focusing on even and odd symplectic supermanifolds with symmetric connections that preserve their symplectic structures.

Contribution

It provides a detailed analysis of Fedosov supermanifolds in normal coordinates, highlighting properties of symplectic supermanifolds with symmetric connections.

Findings

Properties of symplectic supermanifolds in normal coordinates are characterized.

Symmetric connections respecting symplectic structures are analyzed.

Differences between even and odd cases are elucidated.

Abstract

The study of recently introduced Fedosov supermanifolds is continued. Using normal coordinates, properties of even and odd symplectic supermanifolds endowed with a symmetric connection respecting given sympletic structure are studied.