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

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 ${\mathbf{Ca}}^{\prime }$. 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.

17 pages, 1 figure

References in corpus (2)

• Exceptional Lie groups
• Almost complex and almost para-complex Cayley structures on six-dimensional pseudo-Riemannian spheres

Cited by in corpus (1)

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