Helical minimal imbeddings of order 4 into spheres

Kunio SAKAMOTO

doi:10.2969/jmsj/03720315

Kunio SAKAMOTO

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JOURNAL FREE ACCESS

1985 Volume 37 Issue 2 Pages 315-336

DOI https://doi.org/10.2969/jmsj/03720315

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Published: 1985 Received: May 21, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Besse, Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik, 93, Springer, 1978.
2) J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry, North-Holland, Amsterdam-Oxford, 1975.
3) D. Ferus, Symmetric submanifolds of Euclidean space, Math. Ann., 247 (1980), 81-93.
4) S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. II, Interscience, New York-London-Sydney, 1969.
5) J. Little, Manifolds with planar geodesics, J. Differential Geometry, 11 (1976), 265-285.
6) H. Nakagawa, On a certain minimal immersion of a Riemannian manifold into a sphere, Kodai Math. J., 3 (1980), 321-340.
7) B. O'Neill, Isotropic and Kaehler immersions, Canad. J. Math., 17 (1965), 909-915.
8) K. Sakamoto, Planar geodesic immersions, Tohoku Math. J., 29 (1977), 25-56.
9) K. Sakamoto, Helical immersions into a unit sphere, Math. Ann., 261 (1982), 63-80.
10) K. Sakamoto, On a minimal helical immersion into a unit sphere, Advanced Studies in Pure Math., 3 (1984), 193-211.
11) K. Sakamoto, Helical minimal immersions of compact Riemannian manifolds into a unit sphere, to appear in Trans. Amer. Math. Soc.
12) K. Sakamoto, The order of helical minimal imbeddings of strongly harmonic manifolds, to appear in Math. Z.
13) K. Tsukada, Helical geodesic immersions of compact rank one symmetric spaces into spheres, Tokyo J. Math., 6 (1983), 267-285.
14) N. Wallach, Symmetric spaces, edited by W. M. Boothby and G. L. Weiss, Marcel Dekker, New York, 1972.

Right : [1] A. Besse, Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik, 93, Springer, 1978.
[2] J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry, North-Holland, Amsterdam-Oxford, 1975.
[3] D. Ferus, Symmetric submanifolds of Euclidean space, Math. Ann., 247 (1980), 81-93.
[4] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. II, Interscience, New York-London-Sydney, 1969.
[5] J. Little, Manifolds with planar geodesics, J. Differential Geometry, 11 (1976), 265-285.
[6] H. Nakagawa, On a certain minimal immersion of a Riemannian manifold into a sphere, Kodai Math. J., 3 (1980), 321-340.
[7] B. O'Neill, Isotropic and Kaehler immersions, Canad. J. Math., 17 (1965), 909-915.
[8] K. Sakamoto, Planar geodesic immersions, Tohoku Math. J., 29 (1977), 25-56.
[9] K. Sakamoto, Helical immersions into a unit sphere, Math. Ann., 261 (1982), 63-80.
[10] K. Sakamoto, On a minimal helical immersion into a unit sphere, Advanced Studies in Pure Math., 3 (1984), 193-211.
[11] K. Sakamoto, Helical minimal immersions of compact Riemannian manifolds into a unit sphere, to appear in Trans. Amer. Math. Soc.
[12] K. Sakamoto, The order of helical minimal imbeddings of strongly harmonic manifolds, to appear in Math. Z.
[13] K. Tsukada, Helical geodesic immersions of compact rank one symmetric spaces into spheres, Tokyo J. Math., 6 (1983), 267-285.
[14] N. Wallach, Symmetric spaces, edited by W. M. Boothby and G. L. Weiss, Marcel Dekker, New York, 1972.

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