On a type of semi-symmetric non-metric connection on a Riemannian manifold (Q5931831)

A linear connection on a manifold \(M\) is called semi-symmetric if the torsion tensor satisfies \(T(X,Y)=u(X)Y-u(Y)X\), where \(u\) is a 1-form, \(\forall X, Y \in {\mathcal X}(M).\) In the present paper a semi-symmetric, non-metric connection \(\overline{\nabla }\) on a Riemannian manifold \((M,g)\) is introduced. It is studied the curvature tensor of \(M\) with respect to \(\overline {\nabla }\) and the Bianchi identities associated to \(\overline {\nabla }\) are obtained. The Weyl curvature tensor with respect to \(\overline {\nabla }\) is investigated. Conditions under which two semi-symmetric non-metric connections are equal are obtained. Also, the deformation algebra determined by the Levi-Civita connection \(\nabla \) and a semi-symmetric non-metric connection \(\overline {\nabla }\) is considered and its characteristic vector fields are studied.