Abstract:
In this paper, we consider the conharmonic curvature tensor of 6-dimensional planar Hermitian submanifolds of the octave algebra. The Hermitian (and in general case, almost Hermitian) structure on a such submanifold is induced by the so-called Gray–Brown 3-fold vector cross products in Cayley algebra. The main result of the work is the calculation of the so-called spectrum of the conharmonic curvature tensor for an arbitrary 6-dimensional planar Hermitian submanifold of the octave algebra. By the concept of the spectrum of a tensor, we mean the minimal set of its components on the space of the associated $G$-structure that completely determines this tensor.
Keywords and phrases:almost Hermitian structure, conharmonic curvature tensor, Cartan structural equations, 6-dimensional planar submanifold of Cayley algebra.
Fulltext:
PDF file (268 kB)