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Minimal immersions of 2-manifolds into spheres

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References

  1. Benko, K., Kothe, M., Semmler, K.-D. Simon, U.: Eigenvalues of the Laplacian and curvature. Colloq. Math.42, 19–31 (1979)

    Google Scholar 

  2. Calabi, E.: Minimal immersions of surfaces in euclidean spheres. J. Differential Geom.1, 111–125 (1967)

    Google Scholar 

  3. Chern, S.S., do Carmo, M., Kobayashi, S.: Minimal submanifolds of a sphere with second fundamental form of constant length. In: Functional Analysis and Related Fields pp. 59–75. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  4. do Carmo, M.P., Wallach, N.R.: Minimal immersions of spheres into spheres. Ann. Math. (2)93, 43–62 (1971)

    Google Scholar 

  5. Gallot, S.: Équations différentielles charactéristiques de la sphère Ann. Sci. École Norm. Sup. (4)12, 235–267 (1979)

    Google Scholar 

  6. Kozlowski, M.: Geometrische Abschätzungen für kleine Eigenwerte des Laplaceoperators auf fast-sphärischen Rotationsellipsoiden. Dissertation, FB 3 TU Berlin 1983

  7. Lange, F.-J., Simon, U.: Eigenvalues and eigenfunctions of Riemannian manifolds. Proc. Amer. Math. Soc.77, 237–242 (1979)

    Google Scholar 

  8. Lawson, H.B.: Local rigidity theorems for minimal hypersurfaces. Ann. Math. (2)89, 187–197 (1969)

    Google Scholar 

  9. Obata, M.: Certain conditions for a Riemannian manifold to be isometric with a sphere. J. Math. Soc. Japan14, 333–340 (1962)

    Google Scholar 

  10. Simon, U.: Submanifolds with parallel mean curvature vector and the curvature of minimal submanifolds of spheres. Arch. Math. (Basel)29, 106–112 (1977)

    Google Scholar 

  11. Takahashi, T.: Minimal immersions of Riemannian manifolds. J. Math. Soc. Japan18, 380–385 (1966)

    Google Scholar 

  12. Tanno, S.: Some differential equations on Riemannian manifolds. J. Math. Soc. Japan30, 509–531 (1978)

    Google Scholar 

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Kozlowski, M., Simon, U. Minimal immersions of 2-manifolds into spheres. Math Z 186, 377–382 (1984). https://doi.org/10.1007/BF01174890

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  • DOI: https://doi.org/10.1007/BF01174890

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