Some properties of a Ricci quarter symmetric metric connection in a Riemannian manifold
Let \((M,g)\) be a Riemannian manifold and denote by \(L\) its Ricci tensor of type \((1,1)\). A linear metric connection \(\overline{\nabla}\) on \((M,g)\) is said to be Ricci quarter symmetric connection if its torsion \(T\) satisfies \(T(X,Y) = \pi(Y)LX - \pi(X)LY\) where \(\pi\) is a one-form. The authors derive several properties related to the curvature, conformal curvature and Ricci tensor of \(\overline{\nabla}\) when \((M,g)\) is an Einstein space.
scientific article; zbMATH DE number 740382