Circular geodesic submanifolds with parallel mean curvature vector in a non-flat complex space form
An isometric immersion \(f:M\rightarrow N\) is called circular geodesic if any geodesic \(\gamma\) of \(M\) is mapped onto a circle of \(N\). When \(N\) is a real space form, the classification of circular geodesic immersions was performed by \textit{K. Sakamoto} [Tôhoku Math. J., II. Ser. 29, 25-56 (1977; Zbl 0357.53035)]. In the paper under review the ambient space is a nonflat complex space form. It is proven that if the mean curvature vector of \(M\) is parallel in the normal bundle, then the immersion has parallel second fundamental form. The proof relies on previous results of \textit{S. Maeda} and \textit{N. Sato} [Kodai Math. J. 6, 157-166 (1983; Zbl 0531.53041)].
scientific article; zbMATH DE number 1057077