We characterize geodesic spheres with su‰ciently small radii in a complex hyperbolic space of constant holomorphic sectional curvature cð< 0Þ by using their geometric three properties. These properties are based on their contact forms, geodesics and shape operators. These geodesic spheres are the only examples of hypersurfaces of type (A) which are of nonnegative sectional curvature in this ambient space. Moreover, in particular, when À1 e c < 0, the class of these geodesic spheres has just one example of Sasakian space forms.
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