Yildiz, AhmetCetinkaya, Azime2024-08-042024-08-0420140352-96652406-047Xhttps://hdl.handle.net/11616/104173We study a Riemannian manifold M admitting a semisymmetric metric connection (del) over tilde such that the vector field U is a parallel unit vector field with respect to the Levi-Civita connection del. Firstly, we show that ifMis projectively flat with respect to the semisymmetric metric connection (del) over tilde then M is a quasi-Einstein manifold. Also we prove that if R.(P) over tilde = 0 if and only ifMis projectively semisymmetric; if (P) over tilde .R = 0 or R.(P) over tilde-(P) over tilde .R = 0 then Mis conformally flat and quasi-Einstein manifold. Here R, P and (P) over tilde denote Riemannian curvature tensor, the projective curvature tensor of del and the projective curvature tensor of (del) over tilde, respectively.eninfo:eu-repo/semantics/closedAccess[No Keywords]Article291111WOS:000413860500001N/A