On the triviality of the generalized tangent bundle

Fuente: arXiv
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Main Authors: Etayo, Fernando, Gómez-Nicolás, Pablo, Santamaría, Rafael
Format: Preprint
Published: 2026
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author Etayo, Fernando
Gómez-Nicolás, Pablo
Santamaría, Rafael
author_facet Etayo, Fernando
Gómez-Nicolás, Pablo
Santamaría, Rafael
contents We study the relations between the triviality of the tangent bundle $TM$ and the generalized tangent bundle $\mathbb{T}M = TM\oplus T^*M$ 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 Möbius strip, spheres and projective spaces. Finally, we relate the triviality of the generalized tangent bundle to generalized geometric structures.
format Preprint
id arxiv_https___arxiv_org_abs_2605_15818
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On the triviality of the generalized tangent bundle
Etayo, Fernando
Gómez-Nicolás, Pablo
Santamaría, Rafael
Differential Geometry
53D18, 57R22
We study the relations between the triviality of the tangent bundle $TM$ and the generalized tangent bundle $\mathbb{T}M = TM\oplus T^*M$ 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 Möbius strip, spheres and projective spaces. Finally, we relate the triviality of the generalized tangent bundle to generalized geometric structures.
title On the triviality of the generalized tangent bundle
topic Differential Geometry
53D18, 57R22
url https://arxiv.org/abs/2605.15818