A note on curvature-like invariants of some connections on locally decomposable spaces

Abstract

We consider an n-dimensional locally product space with p and q dimensional components (p + q = n) with parallel structure tensor, which means that such a space is locally decomposable. If we introduce a conformal transformation on such a space AB, it will have an invariant curvature-type tensor, the so-called product conformal curvature tensor (PC-tensor). Here we consider two connections, (F, g)-holomorphically semisymmetric one and F-holomorphically semisymmetric one, both with gradient generators. They both have curvature-like invariants and they are both equal to PC-tensor.