A basic inequality for the Tanaka-Webster connection (Q410892)

Summary: For submanifolds tangent to the structure vector field in Sasakian space forms, we establish a basic inequality of Chen type between the main intrinsic invariants of the submanifold (namely, its pseudo-sectional curvature on one side) and the main extrinsic invariant (namely, the squared pseudo-mean curvature on the other side) with respect to the Tanaka-Webster connection. Moreover, involving the pseudo-Ricci curvature and the squared pseudo-mean 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.