On a type of semi-symmetric metric connection on a Riemannian manifold (Q2774614)

The expression for the curvature tensor of the Riemannian manifold that admits a type of semi-symmetric metric connection \(\tilde\nabla\) satisfying conditions \(\tilde R(X,Y)T=0\) and \(\omega(\tilde R(X,Y)Z)=0\), where \(T\) is the torsion tensor of the semi-symmetric connection, \(\tilde R\) is the curvature tensor corresponding to \(\tilde\nabla\) and \(\omega\) is the associated 1-form of \(T\), is obtained. Several results on Riemannian manifolds admitting such kind of semi-symmetric connection are also obtained.