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About generalized complex structures on S6

Abstract: We study the existence of generalized complex structures on the six-dimensional sphere S6. We work with the generalized tangent bundle TS6 --> S6 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 S6 from its usual nearly Kähler structure inherited from the octonions product.

 Fuente: Mediterranean Journal of Mathematics, 2025, 22, 138

 Publisher: Birkhäuser

 Publication date: 18/07/2025

 No. of pages: 19

 Publication type: Article

 DOI: 10.1007/s00009-025-02916-0

 ISSN: 1660-5454,1660-5446

 Publication Url: https://doi.org/10.1007/s00009-025-02916-0

Authorship

PABLO GOMEZ NICOLAS

SANTAMARÍA, RAFAEL