Helical minimal immersions of compact Riemannian manifolds into a unit sphere

Sakamoto, Kunio

doi:10.1090/S0002-9947-1985-0776403-9

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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