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Mean curvature and shape operator of slant immersions in a Sasakian space form.

For submanifolds, in a Sasakian space form, which are tangential to the structure vector Þeld, we establish a basic inequality between squared mean curvature and Ricci curvature. Equality cases are also discussed. Some applications of these results are given for slant, invariant, anti-invariant and CR-submanifolds. We also establish an inequality between the shape operator and the sectional curvature for slant submanifolds in a Sasakian space form. In particular, we give similar results for invariant and anti-invariant submanifolds.