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Ricci curvature of real hypersurfaces in complex hyperbolic space

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*Bang-Yen Chen*

**Address.** Department of Mathematics, Michigan State University, East
Lansing, MI 48824--1027, U S A
**E-mail:** bychen@math.msu.edu

**Abstract.** 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.

**AMSclassification.** Primary 53C40, 53C42; Secondary 53B25.

**Keywords.** Ricci curvature, shape operator, real hypersurface,
algebraic lemma, tubular hypersurface, horosphere, complex hyperbolic space.