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Real supersurfaces in a complex space form with recurrent Ricci tensor. (English) Zbl 1030.53062

Let \((M^n(c),g)\) be a complex space form of complex dimension \(n\) and with non-zero holomorphic sectional curvature \(c\). The author proves that for \(n\geq 3\) there do not exist real hypersurfaces \(P\) in the complex space form \(M\) with recurrent Ricci tensor \(\rho\), i.e., \(\nabla \rho=\alpha \otimes\rho\) where \(\alpha\) is a one-form and \(\nabla\) the induced Levi Civita connection on \(P\).

MSC:

53C40 Global submanifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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