Metric polynomial structures on 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 $\mathbb{T}M:=TM\oplus T^{\ast }M\to M$. In particular, we show the behaviour of various generalized polynomial structures with respect to different metrics on $\mathbb{T}M$, in the frame of $(\alpha ,\epsilon )$-metric structures; and the commutation or anti-commutation of generalized polynomial structures, forming triple structures.