Induced polynomial structures on generalized geometry

Authors: FERNANDO ETAYO, PABLO GOMEZ NICOLAS, RAFAEL SANTAMARIA

Abstract: In this paper, we study different geometric structures that can be defined as section endomorphisms of the generalized tangent bundle $\mathbb TM := TM\oplus T^*M\to M$. This vector bundle admits some structures that arise canonically and other that can be induced from geometric structures defined on the manifold. We comment some well-known examples and present new structures, focusing on the polynomial structures that can be induced in the generalized tangent bundle.

Keywords: Generalized tangent bundle, almost symplectic structure, almost complex structure, almost paracomplex structure, almost product structure, almost tangent structure

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