Helical geodesic immersions of compact rank one symmetric spaces into spheres
type: Item
instance of: scholarly article
title: Helical geodesic immersions of compact rank one symmetric spaces into spheres
zbMATH Open document ID: 0535.53048
author: K. Tsukada
published in: Tokyo Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: The author continues investigations of \textit{K. Sakamoto} [Math. Ann. 261, 63-80 (1982; Zbl 0476.53033)] on helical geodesics immersions into unit spheres. An isometric immersion \(M\to S^ n\) is a helical geodesic immersion, iff the images of all unit speed geodesics of M are congruent helices of \(S^ n\). In the paper under review the author proves that every helical geodesic, minimal immersion from a real analytic strongly harmonic manifold into \(S^ n\) is congruent to one of the standard immersions already described by \textit{A. L. Besse} in ''Manifolds all of whose geodesics are closed'' (1978; Zbl 0387.53010). He also classifies the helical geodesic immersions from compact rank one symmetric spaces into \(S^ n\).
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 3850040
zbMATH Keywords: minimal immersions
zbMATH Keywords: helical geodesics immersions
zbMATH Keywords: harmonic manifold
zbMATH Keywords: rank one symmetric spaces
reviewed by: Helmut Reckziegel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270213869
OpenAlex ID: W1965188822
DOI: 10.3836/TJM/1270213869
Recommended article: Helical geodesic immersions of semi-Riemannian manifolds
Recommended article: Helical Minimal Immersions of Compact Riemannian Manifolds into a Unit Sphere
Recommended article: Generalized helical immersions of a Riemannian manifold all of whose geodesics are closed into a Euclidean space
Recommended article: Helgason spheres of compact symmetric spaces and immersions of finite type
Recommended article: Q3717783
Recommended article: Helical geodesic immersions into complex space forms
Recommended article: Q3333689
Recommended article: Helical immersions into a Euclidean space
Recommended article: Q5199289
Recommended article: Q3021873
description: scientific article; zbMATH DE number 3850040