ON SPECTRA OF SOME TENSORS OF SIX-DIMENSINAL KÄHLERIAN AND NEARLY-KÄHLERIAN SUBMANIFOLDS OF CAYLEY ALGEBRA

Abstract

Six-dimensional Kählerian and nearly-Kählerian submanifolds of Cayley algebra are considered. Spectra of some classical tensors of such submanifolds of the octave algebra are computed. It is proved that a nearly-Kählerian six-dimensional submanifold of Cayley algebra is conharmonically flat if and only if it is holomorphically isometric to the complex Euclidean space  with a canonical Kählerian structure.

2010 MSC: 53 C55, 53 C40.