On almost complex surfaces of the nearly Kaehler 6-sphere. II
type: Item
instance of: scholarly article
title: On almost complex surfaces of the nearly Kaehler 6-sphere. II
zbMATH Open document ID: 0677.53063
author: Leopold Verstraelen
author: Luc Vrancken
author: Franki Dillen
published in: Kodai Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: On a 6-dimensional unit sphere \(S^ 6(1)\) a nearly Kaehler structure J can be defined in a natural way, making use of the Cayley numbers. In these two papers we consider almost complex surfaces M in \(S^ 6(1)\), i.e. surfaces whose tangent bundle is invariant under J. In [Kodai Math. J. 6, 174-185 (1983; Zbl 0517.53055)], \textit{K. Sekigawa} shows that, if an almost complex surface M has constant curvature K, the \(K=0\), \(K=1/6\), or \(K=1\). The problem of U. Simon is given by: ``Let M be an almost complex compact surface of \(S^ 6(1)\) with Gaussian curvature K. If 1/6\(\leq K\leq 1\), then \(K=1/6\) or \(K=1?\) If \(0\leq K\leq 1/6\), then \(K=0\) or \(K=1/6?''\) In these papers we give an affirmative answer to both questions. Our main tool is the integral formula of A. Ros. The results have been announced in Bull. Am. Math. Soc., New Ser. 19, 433-438 (1988; Zbl 0655.53052).
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4109567
zbMATH Keywords: nearly Kaehler structure
zbMATH Keywords: Cayley numbers
zbMATH Keywords: almost complex surfaces
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037456
OpenAlex ID: W2056294707
cites work: Construction and Properties of Some 6-Dimensional Almost Complex Manifolds
cites work: Minimal immersions of surfaces into spheres
cites work: Q3833207
cites work: Almost hermitian structure on \(S^6\)
cites work: Minimal varieties and almost Hermitian submanifolds
cites work: Almost Complex Submanifolds of the Six Sphere
cites work: Minimal surfaces in a sphere with Gaussian curvature not less than 1/6
cites work: A characterization of seven compact Kähler submanifolds by holomorphic pinching
cites work: Almost complex submanifolds of a 6-dimensional sphere
DOI: 10.2996/KMJ/1138037456
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description: scientific article; zbMATH DE number 4109567