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Real hypersurfaces of complex space forms in terms of Ricci *-tensor. (English) Zbl 1046.53037

In the present paper the author studies real hypersurfaces in a complex space form \(M_{n}(c)\) in terms of a generalization of the Ricci tensor (the so-called Ricci \(*\)-tensor introduced by Shun-ichi Tachibana in [Tôhoku Math. J., II. Ser. 11, 247–265 (1959; Zbl 0090.38603)].
The main result is a classification of \(*\)-Einstein real hypersurfaces in \(M_{n}(c)\) whose structure vector is a principal curvature vector.

MSC:

53C40 Global submanifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)

Citations:

Zbl 0090.38603
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References:

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