One of the problem considered in Riemannian geometry is checking inequalities for submanifolds in various space forms endowed with a semi-symmetric metric connection. If the torsion tensor of linear connection on Riemannian manifold (M,g), satisfies X,Y)= (Y)X-?(X)Y for any vector fields X,Y and 1-form ? , then the connection is called a semi-symmetric connection. If g=0 then is called asemi-symmetric metric connection on M. Most of these inequalities are to explained relations between the extrinsic geometry and intrinsic geometry of a submanifold. Among all the submanifold properties mean, sectional, scalar and Ricci curvatures are usually present in the inequalities. The most famous inequalities of the submanifold are Chen inequality. In fact the first Chen inequality representer a inequality between scalar curvature and mean curvature. The special form of this inequality is determined by properties of space forms. For example, a Riemannian manifold (M,g) of quasi-constant curvature is a Riemannian manifold with the curvature tensor satisfying in the special condition on the curvature tensor .