1,508 research outputs found
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 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
- …