Helical geodesic immersions of compact rank one symmetric spaces into spheres
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 \(S^ n\).
scientific article; zbMATH DE number 3850040
scientific article