Loo, Tee-How Real supersurfaces in a complex space form with recurrent Ricci tensor. (English) Zbl 1030.53062 Glasg. Math. J. 44, No. 3, 547-550 (2002). 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 \(P\). Reviewer: L.Vanhecke (Leuven) Cited in 2 Documents MSC: 53C40 Global submanifolds 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:complex space form; holomorphic sectional curvature; recurrent Ricci tensor; Levi Civita connection PDFBibTeX XMLCite \textit{T.-H. Loo}, Glasg. Math. J. 44, No. 3, 547--550 (2002; Zbl 1030.53062)