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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Helical minimal immersions of compact Riemannian manifolds into a unit sphere


Author: Kunio Sakamoto
Journal: Trans. Amer. Math. Soc. 288 (1985), 765-790
MSC: Primary 53C42; Secondary 53C40
MathSciNet review: 776403
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Abstract: An isometric immersion of a Riemannian manifold $ M$ into a Riemannian manifold $ \overline M $ is called helical if the image of each geodesic has constant curvatures which are independent of the choice of the particular geodesic. Suppose $ M$ is a compact Riemannian manifold which admits a minimal helical immersion of order $ 4$ into the unit sphere. If the Weinstein integer of $ M$ equals that of one of the projective spaces, then $ M$ is isometric to that projective space with its canonical metric.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0776403-9
PII: S 0002-9947(1985)0776403-9
Keywords: Helical immersions, strongly harmonic manifolds, geodesics, Blaschke structure, cut loci, second fundamental forms
Article copyright: © Copyright 1985 American Mathematical Society