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