The order of helical minimal imbeddings of strongly harmonic manifolds
type: Item
instance of: scholarly article
title: The order of helical minimal imbeddings of strongly harmonic manifolds
zbMATH Open document ID: 0598.53054
DOI: 10.1007/BF01162702
author: Kunio Sakamoto
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173755
review text: Main theorem: Let \(f: M\to S^ n\) be a helical minimal imbedding of order d of a compact Riemannian manifold into the unit sphere (i.e. all geodesics are congruent in \(S^ n\), and have constant Frenet curvatures of which exactly d-1 are non-zero). If \(<f(x),f(y)>=F(d(x,y))\) with a monotone decreasing function F, and f is not totally geodesic, then d is even.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 3964930
zbMATH Keywords: W-curves
zbMATH Keywords: helical imbedding
zbMATH Keywords: minimal imbedding
reviewed by: Dirk Ferus
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3964930