Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE RIGIDITY OF MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC SPACE

  • Cao, Shunjuan (Department of Mathematics Zhejiang Agricultural and Forestry University)
  • Received : 2011.06.03
  • Published : 2013.01.31
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Abstract

In the present paper, we discuss the rigidity phenomenon of closed minimal submanifolds in a locally symmetric Riemannian manifold with pinched sectional curvature. We show that if the sectional curvature of the submanifold is no less than an explicitly given constant, then either the submanifold is totally geodesic, or the ambient space is a sphere and the submanifold is isometric to a product of two spheres or the Veronese surface in $S^4$.

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References

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