Geometry of almost Cliffordian manifolds: classes of subordinated connections

An almost Clifford and an almost Cliffordian manifold is a G –structure based on the definition of Clifford algebras. An almost Clifford manifold based on O := Cl(s, t) is given by a reduction of the structure group GL(km, R) to GL(m, O) , where k = 2^s+t and m ∈ N. An almost Cliffordian manifold is given by a reduction of the structure group to GL(m, O)GL(1, O). We prove that an almost Clifford manifold based on O is such that there exists a unique subordinated connection, while the case of an almost Cliffordian manifold based on O is more rich. A class of distinguished connections in this case is described explicitly.