Real Hypersurfaces With Constant Principal Curvatures in Complex Hyperbolic Spaces

Abstract

We present the classification of all real hypersurfaces in complex hyperbolic space CH n , n 3, with three distinct constant principal curvatures.

Real Hypersurfaces in a Non-Flat Complex Space Form With Lie Recurrent Structure Jacobi Operator

“…The Hopf real hypersurface which satisfies the previous conditions is that of type B in CH n . Substituting the eigenvalues of it in λ = −ν leads to a contradiction (for the eigenvalues see [1]). …”

“…In [10], [11] Takagi was the first who studied and classified homogeneous real hypersurfaces in CP n and showed that they could be divided into six types, namely (A 1 ), (A 2 ), (B), (C), (D) and (E). In the case of CH n , Berndt in [1] classified real hypersurfaces with constant principal curvatures, when ξ is principal. Such real hypersurfaces are homogeneous.…”

ON THE LIE DERIVATIVE OF REAL HYPERSURFACES IN ℂP2AND ℂH2WITH RESPECT TO THE GENERALIZED TANAKA-WEBSTER CONNECTION

“…These real hypersurfaces are Hopf ones with constant principal curvatures. In case of CH n , the study of real hypersurfaces with constant principal curvatures, was started by Montiel in [5] and completed by Berndt in [1]. They are divided into two types, namely (A) and (B), depending on the number of constant principal curvatures.…”

Real Hypersurfaces With Cyclic-Parallel Structure Jacobi Operators in a Nonflat Complex Space Form

“…Those hypersurfaces have a lot of nice geometric properties (see Berndt [1] and Montiel and Romero [9]). In 2007 Berndt and Tamaru [2] classified all homogeneous real hypersurfaces in H n C.…”