C-totally real submanifolds of Sasakian space forms
type: Item
instance of: scholarly article
title: C-totally real submanifolds of Sasakian space forms
zbMATH Open document ID: 0654.53062
author: Luc Vrancken
author: Franki Dillen
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1990-01-01T00:00:00Z
review text: On an odd-dimensional unit sphere \(S^{2n+1}(1)\) one can define a Sasakian structure in a natural way. In this paper we prove that, if the sectional curvatures \(K\) of an \(n\)-dimensional, compact, minimal, C-totally real submanifold \(M^n\) of \(S^{2n+1}(1)\) satisfy \(0\leq K\leq 1\), then either \(K\equiv 1\) \((M^n\) is totally geodesic) or \(K\equiv 0\) \((M^n\) is flat). Finally we give examples of submanifolds satisfying \(K\equiv 0\) and \(K\equiv 1\), as well as an example showing that the upper bound \(K\leq 1\) is needed.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 4067813
zbMATH Keywords: minimal submanifold
zbMATH Keywords: Sasakian structure
zbMATH Keywords: sectional curvatures
zbMATH Keywords: C-totally real submanifold
reviewed by: Franki Dillen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4067813