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A characterization of pseudo-Einstein real hypersurfaces of a complex space form

Kon M

Journal of Applied Analysis

2013

Vol. 19, nr 2

167--179

We give a characterization of pseudo-Einstein real hypersurfaces of a complex space form. We prove that if the Ricci tensor S of a real hypersurface M of a complex space form with constant principal curvatures satisfies S(X, Y)=ag(X, Y) for any X, Y ∈ T 0(x), where a is a function and T0 is the holomorphic distribution on M, then M is a pseudo-Einstein real hypersurface.