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

Fuente: arXiv
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Main Authors: Etayo, Fernando, Gómez-Nicolás, Pablo, Santamaría, Rafael
Format: Preprint
Published: 2024
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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 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_05681
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle About generalized complex structures on $\mathbb S^6$
Etayo, Fernando
Gómez-Nicolás, Pablo
Santamaría, Rafael
Differential Geometry
53D18, 53C15
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.
title About generalized complex structures on $\mathbb S^6$
topic Differential Geometry
53D18, 53C15
url https://arxiv.org/abs/2405.05681