2-type integral surfaces in \(S^ 5(1)\)
type: Item
instance of: scholarly article
title: 2-type integral surfaces in \(S^ 5(1)\)
zbMATH Open document ID: 0763.53055
author: Christos Baikoussis
author: David E. Blair
published in: Tokyo Journal of Mathematics
publication date: 1992-09-27T00:00:00Z
review text: Let \(S^ 5\) be the unit hypersphere of the Euclidean 6-space \(E^ 6\). Consider \(S^ 5\) as a Sasakian manifold with the canonical contact 1- form \(\eta\). A surface \(M\) in \(S^ 5\) is called an integral surface if \(\eta\) restricted to \(M\) vanishes identically. In this paper, the authors classify integral surfaces of \(S^ 5\) which are mass-symmetric and of 2- type [in the sense of the reviewer, Total mean curvature and submanifolds of finite type (1984; Zbl 0537.53049)]. They show that a mass-symmetric 2-type integral surface \(M\) of \(S^ 5\) lies fully in \(S^ 5\) and is the product of a plane circle and a helix of order 4, or the product of two circles. Moreover, \(M\) belongs to a 1-parameter family of such surfaces. Furthermore, \(M\) is not stationary.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 60846
zbMATH Keywords: Sasakian manifold
zbMATH Keywords: canonical contact 1-form
zbMATH Keywords: mass-symmetric
reviewed by: Bang-Yen Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270130378
OpenAlex ID: W2032357132
Wikidata QID: Q125618800
DOI: 10.3836/TJM/1270130378
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description: scientific article; zbMATH DE number 60846