2000 character limit reached
About generalized complex structures on $\mathbb S^6$ (2405.05681v3)
Published 9 May 2024 in math.DG
Abstract: We study the existence of generalized complex structures on the six-dimensional sphere $\mathbb S6$. We work with the generalized tangent bundle $\mathbb T\mathbb S6\to \mathbb S6$ 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 $\mathbb S6$ from its usual nearly K\"ahler structure inherited from the octonions product.
- M. Gualtieri. Generalized complex geometry. Ann. of Math. (2) 174, 75–123 (2011).
- N. Hitchin. Generalized Calabi-Yau manifolds. Q. J. Math. 54, 281–308 (2003).
- C. Ida and A. Manea. On the integrability of generalized almost para-Norden and para-Hermitian structures. Mediterr. J. Math. 14, Paper No. 173 (2017).
- A. Nannicini. Calibrated complex structures on the generalized tangent bundle of a Riemannian manifold. J. Geom. Phys. 56, 903–916 (2006).
- A. Nannicini. Almost complex structures on cotangent bundles and generalized geometry. J. Geom. Phys. 60, 1781–1791 (2010).
- W. A. Poor. Differential geometric structures. McGraw-Hill Book Co., New York (1981).
- A. Wade. Dirac structures and paracomplex manifolds. C. R. Math. Acad. Sci. Paris 338, 889–894 (2004).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.