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arXiv · 1807.08395

Almost complex and almost para-complex Cayley structures on six-dimensional pseudo-Riemannian spheres

N. K. Smolentsev
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Abstract

In this paper we study almost complex and almost para-complex Cayley structures on six-dimensional pseudo-Riemannian spheres in the space of purely imaginary octaves of the split Cayley algebra $\mathbf{Ca}'$. It is shown that the Cayley structures are non-integrable, their basic geometric characteristics are calculated. In contrast to the usual Riemann sphere $\mathbb{S}^6$, there exist (integrable) complex structures and para-complex structures on the pseudospheres under consideration.

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N. K. Smolentsev. 2018-07-23. Almost complex and almost para-complex Cayley structures on six-dimensional pseudo-Riemannian spheres. https://doi.org/10.17223/19988621%2F53%2F3

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