On a type of semi-symmetric non-metric connection (Q2716739)

Let \((M,g)\) be a Riemannian manifold with Levi-Civita connection \(\nabla\) and \(U,A\) be two vector fields on \(M\). The authors define a semi-symmetric non-metric connection \(\overline\nabla\) by the formula \(\overline \nabla_X Y=\nabla_X Y+g(Y,U)X- g(X,Y)U-g (A,X)Y-g (Y,A)X\). First of all they deduce that the torsion of \(\overline\nabla\) has some properties analogous to the case of the classical semi-symmetric connection. Then the authors study in detail the curvature tensor and the Bianchi identities of \(\overline\nabla\). Finally they characterize the induced connection on a hypersurface of \(M\).