English

On the triviality of the generalized tangent bundle

Differential Geometry 2026-05-18 v1

Abstract

We study the relations between the triviality of the tangent bundle TMTM and the generalized tangent bundle TM=TMTM\mathbb{T}M = TM\oplus T^*M of a manifold. We show that the generalized tangent bundle of a paralellizable manifold is trivial. We also prove that the converse implication does not hold, by studying the cases of the M\"obius strip, spheres and projective spaces. Finally, we relate the triviality of the generalized tangent bundle to generalized geometric structures.

Keywords

Cite

@article{arxiv.2605.15818,
  title  = {On the triviality of the generalized tangent bundle},
  author = {Fernando Etayo and Pablo Gómez-Nicolás and Rafael Santamaría},
  journal= {arXiv preprint arXiv:2605.15818},
  year   = {2026}
}