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A THEOREM OF G-INVARIANT MINIMAL HYPERSURFACES WITH CONSTANT SCALAR CURVATURES IN Sn+1

  • So, Jae-Up (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University)
  • Received : 2009.07.13
  • Accepted : 2009.09.14
  • Published : 2009.09.25

Abstract

Let $G\;=\;O(k){\times}O(k){\times}O(q)$ and let $M^n$ be a closed G-invariant minimal hypersurface with constant scalar curvature in $S^{n+1}$. Then we obtain a theorem: If $M^n$ has 2 distinct principal curvatures at some point p, then the square norm of the second fundamental form of $M^n$, S = n.

Keywords

scalar curvature;G-invariant minimal hypersurface;square norm

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