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On the topology of a compact submanifold of a sphere with bounded second fundamental form

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Abstract

Leth be the second fundamental form of a compact submanifold of a unit sphere. We show that if ‖h(u, u)‖2<1/3 holds for any unit tangent vectoru at any point on the submanifold then it is a homotopy sphere.

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References

  1. H. Gauchman, Minimal submanifolds of a sphere with bounded second fundamental form. Trans. Amer. Math. Soc. 298 (1986) 779–791

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  2. H.B. Lawson and J. Simons, On stable currents and their application to global problems in real and complex geometry. Ann. of Math. 98 (1973) 427–450

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  1. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 0511, Singapore

    Pui-Fai Leung

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  1. Pui-Fai Leung
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Leung, PF. On the topology of a compact submanifold of a sphere with bounded second fundamental form. Manuscripta Math 79, 183–185 (1993). https://doi.org/10.1007/BF02568337

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  • DOI: https://doi.org/10.1007/BF02568337

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