On the triviality of the generalized tangent bundle
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866913132116443136 |
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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 |