Some theorems in an almost product and almost decomposable manifold (Q760677)

Let M be an almost product and almost decomposable Riemannian manifold. From the defining tensor of the almost product structure, the curvature tensor of the almost product structure, the curvature tensor of the Levi- Civita connection and its covariant derivatives some further tensors can be defined (e.g. the Weyl curvature tensor, the H-projective tensor, the conharmonic tensor etc.). In this paper recurrence conditions on these tensors and their relations are studied.