Circular geodesic submanifolds with parallel mean curvature vector in a non-flat complex space form
type: Item
instance of: scholarly article
title: Circular geodesic submanifolds with parallel mean curvature vector in a non-flat complex space form
zbMATH Open document ID: 0889.53040
author: Sadahiro Maeda
author: Ryoichi Takagi
published in: Proceedings of the Japan Academy. Series A
publication date: 1998-05-29T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1057077
zbMATH Keywords: complex space form
zbMATH Keywords: parallel mean curvature vector
zbMATH Keywords: geodesic submanifold
zbMATH Keywords: circle
reviewed by: Liviu Ornea
MaRDI profile type: Publication
full work available at URL: pjaa.73.55
OpenAlex ID: W2022895934
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cites work: Q3667562
DOI: 10.3792/PJAA.73.55
description: scientific article; zbMATH DE number 1057077