MANIFOLDS ADMITTING A STRUCTURE OF FOUR DIMENTIONAL ALGEBRA OF AFFINORS

Abstract

The purpose of this note is to describe some properties of manifolds endowed with an almost tangent structure $T, T^2 = 0$ and an almost complex structure $J, J^2 = {−E}, E = id$. We consider a linear connection $\nabla$ on $N$, which is compatible with the algebraic structure, i.e. $\nabla J = 0, \nabla T = 0$. The existence of ideals in corresponding algebra implies the existence of autoparallel submanifolds of N.