in the first part of this paper, some theorems are given for a riemannian manifold with semi-symmetric metric connection. in the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. we obtain some properties of this manifold having the vectors mentioned above.

We introduced a class of conformally invariant Ehresmann connections so–called L-horizontal endomorphism in [7]. Using this class, we define conformally invariant manifolds: Wagner–type manifold and locally Minkowski–type manifold as special generalized Berwald manifolds. Then a generalization of Hashiguchi–Ichijyō’s Theorems to Wagner–type manifolds is presented. Mathematics Subject Classifica...

Conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent, $(GR)_n$ structure are completely classified in this short report. A conformally recurrent manifold is shown to be either a de Sitter space or an anti-de space. In particular, spacetime must spacetime.