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Rigidity of minimal surfaces inS 3

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Abstract

Isometric deformations of compact minimal surfaces in the standard three-sphere are studied. It is shown that a given surface admits only finitely many noncongruent minimal immersions intoS 3 with the same first fundamental form.

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References

  1. Bryant, R.: Minimal Surfaces of Constant Curvature inS 3. Trans. Amer. Math. Soc., 290 No. 1, 259–271, 1985

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  2. Hsiang, W-Y. and Lawson Jr., H.B.: Minimal Submanifolds of Low Cohomogeneity. Jour. of Differential Geometry, 5, 1–38, 1971

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  3. Lawson Jr., H.B.: Complete Minimal Surfaces inS 3. Annals of Mathematics, 90, 335–374, 1970

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  1. Jayakumar Ramanathan

    Present address: Dept. of Mathematics, University of Illinois, Champaign-Urbana, 1409 W. Green St., 61801, Urbana, IL

Authors and Affiliations

  1. Dept. of Mathematics, University of Michigan, 48109, Ann Arbor, Michigan

    Jayakumar Ramanathan

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  1. Jayakumar Ramanathan
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Ramanathan, J. Rigidity of minimal surfaces inS 3 . Manuscripta Math 60, 417–422 (1988). https://doi.org/10.1007/BF01258661

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  • DOI: https://doi.org/10.1007/BF01258661

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