arXiv subjects

Pablo Gómez-Nicolás

Publications and source records attributed to Pablo Gómez-Nicolás.

3 recordsLinked to original sources

arXiv2026

On the triviality of the generalized tangent bundle

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.

math.DG↗

arXiv2025

About generalized complex structures on $\mathbb S^6$

We study the existence of generalized complex structures on the six-dimensional sphere $\mathbb S^6$. We work with the generalized tangent bundle $\mathbb T\mathbb S^6\to \mathbb S^6$ and define the integrability of generalized geometric structures in terms of the Dorfman bracket. Specifically, we prove that there is not a direct way to induce a generalized complex structure on $\mathbb S^6$ from its usual nearly Kähler structure inherited from the octonions product.

math.DG↗

arXiv2022

Metric polynomial structures on generalized geometry

In this document, we study the interaction between different geometric structures that can be defined as morphisms of sections of the generalized tangent bundle $\mathbb TM:= TM\oplus T^*M\to M$. In particular, we show the behaviour of various generalized polynomial structures with respect to different metrics on $\mathbb TM$, in the frame of $(α, \varepsilon)$-metric structures; and the commutation or anti-commutation of generalized polynomial structures, forming triple structures.

math.DG↗