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Keywords:
Ricci curvature; shape operator; real hypersurface; algebraic lemma; tubular hypersurface; horosphere; complex hyperbolic space
Ricci curvature; shape operator; real hypersurface; algebraic lemma; tubular hypersurface; horosphere; complex hyperbolic space
Summary:
First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.
References:
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