On totally real surfaces of the nearly Kähler 6-sphere
type: Item
instance of: scholarly article
title: On totally real surfaces of the nearly Kähler 6-sphere
zbMATH Open document ID: 0658.53054
DOI: 10.1007/BF00181497
author: Leopold Verstraelen
author: Luc Vrancken
author: Franki Dillen
author: Barbara Opozda
published in: Geometriae Dedicata
publication date: 1988-01-01T00:00:00Z
review text: In Proc. Am. Math. Soc. 99, 741-749 (1987; Zbl 0618.53046) the present authors have studied totally real 3-dimensional submanifolds of the nearly Kähler 6-sphere. This paper is devoted to the study of totally real surfaces of the nearly Kähler 6-sphere. The authors prove that if M is a minimal 2-dimensional totally real submanifold of \(S^ 6(1)\) and M is homeomorphic to a sphere, then M is totally geodesic. Using this fact, they show that if M is compact and has non-negative Gaussian curvature K, then either \(K=0\), or \(K=1\). Finally, the authors dicuss some examples.
reviewed by: E. D. Rodionov
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 4076004
zbMATH Keywords: totally real
zbMATH Keywords: nearly Kähler 6-sphere
zbMATH Keywords: totally geodesic
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181497
OpenAlex ID: W2030688044
description: scientific article; zbMATH DE number 4076004