Lie Groupoids and Generalized Almost Subtangent Manifolds

TL;DR

This paper explores the relationship between generalized almost subtangent manifolds and Lie groupoids, establishing equivalences among their integrability conditions and compatibility criteria with symplectic structures.

Contribution

It provides new insights into the integrability and compatibility conditions linking generalized subtangent manifolds with Lie groupoids.

Findings

Equivalence between integrability conditions and symplectic compatibility.

Characterization of generalized subtangent maps via Lie groupoids.

Conditions for the compatibility of source and target maps with symplectic forms.

Abstract

In this paper, we show that there is a close relationship between generalized subtangent manifolds and Lie groupoids. We obtain equivalent assertions among the integrability conditions of generalized almost subtangent manifolds, the condition of compatibility of source and target maps of symplectic groupoids with symplectic form and generalized subtangent maps.