Quarter-symmetric generalized metric connections on a generalized Riemannian manifold

We define and study the quarter-symmetric connection preserving the generalized metric G in the generalized Riemannian manifold. It is proved that skew-symmetric part F of the generalized metric G in the generalized Riemannian manifold with the quarter-symmetric generalized metric connection is closed and hence the even-dimensional manifold is a symplectic manifold. We also observed the properties of curvature tensors and connection transformations in which the Riemannian tensor of the Levi-Civita connection is invariant. Finally, we observed the quarter-symmetric connection with a special conditions.