Mathematische Annalen

, Volume 261, Issue 1, pp 63–80 | Cite as

Helical immersions into a unit sphere

  • Kunio Sakamoto


Unit Sphere 
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  1. 1.
    Allamigeon, A.: Propriétés globales des espaces de Riemann harmoniques. Ann. Inst. Fourier15, 91–132 (1965)Google Scholar
  2. 2.
    Berger, M., Gaudechon, P., Mazet, E.: Le spectre d'une variété Riemannienne. Lecture Notes, Vol. 194. Berlin, Heidelberg, New York: Springer 1971Google Scholar
  3. 3.
    Besse, A.: Manifolds all of whose geodesics are closed. Ergebnisse der Mathematik, Bd. 93. Berlin, Heidelberg, New York: Springer 1978Google Scholar
  4. 4.
    Ferus, D.: Symmetric submanifolds of Euclidean space. Math. Ann.247, 81–93 (1980)Google Scholar
  5. 5.
    Helgason, S.: Differential geometry and symmetric spaces. New York, London: Academic Press 1962Google Scholar
  6. 6.
    Hong, S.L.: Isometric immersions of manifolds with plane geodesics into Euclidean space. J. Differential Geometry8, 259–278 (1973)Google Scholar
  7. 7.
    Kobayahsi, S., Nomizu, K.: Foundations of differential geometry. II. New York, London, Sydney: Interscience 1969Google Scholar
  8. 8.
    Little, J.A.: Manifolds with planar geodesics. J. Differential Geometry11, 265–285 (1976)Google Scholar
  9. 9.
    Michel, D.: Comparison des notions de variétés Riemanniennes globalement harmoniques et fortement harmoniques. C.R. Acad. Sci. Paris, Ser. A282, 1007–1010 (1976)Google Scholar
  10. 10.
    Nakagawa, H.: On a certain minimal immersion of a Riemannian manifold into a sphere. Kodai Math. J.3, 321–340 (1980)Google Scholar
  11. 11.
    O'Neill, B.: Isotropic and Kaeler immersions. Canad. J. Math.17, 909–915 (1965)Google Scholar
  12. 12.
    Ruse, H.S., Walker, A.G., Willmore, T.J.: Harmonic spaces. Consiglio Nacionale delle Ricerche. Monographie Mathematiche 8, Roma: Edizioni Cremonese 1961Google Scholar
  13. 13.
    Sakamoto, K.: Planar geodesic immersions. Tôhoku Math. J.29, 25–56 (1977)Google Scholar
  14. 14.
    Takahashi, T.: Minimal immersions of Riemannian manifolds. J. Math. Soc. Japan18, 203–215 (1968)Google Scholar
  15. 15.
    Wallach, N.R.: Symmetric spaces. Boothby, W.M., Weiss, G.L., eds. New York: Marcel Dekker 1972Google Scholar
  16. 16.
    Wolter, F.E.: Distance function and cut loci on a complete Riemannian manifold. Arch. Math.32, 92–96 (1979)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Kunio Sakamoto
    • 1
  1. 1.Department of MathematicsTokyo Institute of TechnologyTokyoJapan

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