A Basic Inequality for the Tanaka-Webster Connection

For submanifolds tangent to the structure vector field in Sasakian space forms, we establish a Chen’s basic inequality between the main intrinsic invariants of the submanifold namely, its pseudosectional curvature and pseudosectional curvature on one side and the main extrinsic invariant namely, squared pseudomean curvature on the other side with respect to the TanakaWebster connection. Moreover, involving the pseudo-Ricci curvature and the squared pseudomean curvature, we obtain a basic inequality for submanifolds of a Sasakian space form tangent to the structure vector field in terms of the Tanaka-Webster connection.