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.
Generalized tangent bundle, almost symplectic structure, almost complex structure, almost paracomplex structure, almost product structure, almost tangent structure
ETAYO, FERNANDO; NICOLAS, PABLO GOMEZ; and SANTAMARIA, RAFAEL
"Induced polynomial structures on generalized geometry,"
Turkish Journal of Mathematics: Vol. 46:
4, Article 28.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss4/28