HOMOGENEOUS REAL HYPERSURFACES IN A COMPLEX HYPERBOLIC SPACE WITH FOUR CONSTANT PRINCIPAL CURVATURES

Abstract

We deal with the classification problem of real hypersurfaces in a complex hyperbolic space. In order to classify real hypersurfaces in a complex hyperbolic space we characterize a real hypersurface M in Hn(C) whose structure vector field is not principal. We also construct extrinsically homogeneous real hypersurfaces with four distinct curvatures and their structure vector fields are not principal.

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