MANIFOLDS ADMITTING A STRUCTURE OF FOUR DIMENTIONAL ALGEBRA OF AFFINORS (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2016)
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 $ abla$ on $N$, which is compatible with the algebraic structure, i.e. $ abla J = 0, abla T = 0$. The existence of ideals in corresponding algebra implies the existence of autoparallel submanifolds of N.