Basic properties of Fedosov supermanifolds
B. Geyer, P.M. Lavrov
TL;DR
This paper explores the fundamental properties of Fedosov supermanifolds, which are supermanifolds with a symplectic structure and a compatible connection, extending classical Fedosov geometry into the supersymmetric realm.
Contribution
It generalizes the concept of Fedosov manifolds to supermanifolds, analyzing their basic properties and the implications of symplectic structures in supersymmetric geometry.
Findings
Properties of supermanifolds with symplectic structures are established.
The compatibility of connections with symplectic forms in supergeometry is characterized.
Foundations for further study of Fedosov supermanifolds are laid out.
Abstract
Basic properties of even (odd) supermanifolds endowed with a connection respecting a given symplectic structure are studied. Such supermanifolds can be considered as generalization of Fedosov manifolds to the supersymmetric case.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows