Metric polynomial structures on generalized geometry

TL;DR

This paper explores the interactions and properties of polynomial geometric structures within generalized geometry, focusing on their behavior under various metrics and their algebraic relations.

Contribution

It introduces a detailed analysis of generalized polynomial structures, their metric interactions, and their algebraic properties in the context of generalized tangent bundles.

Findings

Behavior of polynomial structures under different metrics

Conditions for commutation and anti-commutation of structures

Characterization of triple structures in generalized geometry

Abstract

In this document, we study the interaction between different geometric structures that can be defined as morphisms of sections of the generalized tangent bundle $\mathbb TM:= TM\oplus T^*M\to M$. In particular, we show the behaviour of various generalized polynomial structures with respect to different metrics on $\mathbb TM$, in the frame of $(\alpha, \varepsilon)$-metric structures; and the commutation or anti-commutation of generalized polynomial structures, forming triple structures.