# MANIFOLDS ADMITTING A STRUCTURE OF FOUR DIMENTIONAL ALGEBRA OF AFFINORS

 Title MANIFOLDS ADMITTING A STRUCTURE OF FOUR DIMENTIONAL ALGEBRA OF AFFINORS Publication Type Journal Article Year of Publication 2016 Authors Hristov A, Kostadinov G Journal Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique Volume 103 Pagination 89-95 ISSN 0205-0808 Keywords affinely connected manifold, algebra of fiber-preserving operators, Four dimentional associative algebra 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. 2010 MSC 53C15, 58A30, 53C07
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