## Helical minimal immersions of compact Riemannian manifolds into a unit sphere

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- by Kunio Sakamoto
- Trans. Amer. Math. Soc.
**288**(1985), 765-790 - DOI: https://doi.org/10.1090/S0002-9947-1985-0776403-9
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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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## Bibliographic Information

- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**288**(1985), 765-790 - MSC: Primary 53C42; Secondary 53C40
- DOI: https://doi.org/10.1090/S0002-9947-1985-0776403-9
- MathSciNet review: 776403