On Finsler spaces with the curvature tensors Phijk and Shijk satisfying special conditions

The curvature tensor P_hijk of a Finsler space has a mixed character, while R_hijk is horizontal and S_hijk is vertical in a sense. Because we have no resemblance to P_hijk in the Riemannian geometry, the problem to study it may be rather difficult. Recently the problem of P_hijk has also been raised from the viewpoint of physics. Continuing previous paper [7], we study P_hijk satisfying some special conditions and the possibility of deducing the so-called Ricci tensor from P_hijk. Further a special form of the curvature tensor S_hijk is proposed and a problem relating to P_hijk is studied.