Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LINEAR WEINGARTEN HYPERSURFACES IN RIEMANNIAN SPACE FORMS

  • Chao, Xiaoli (Department of Mathematics Southeast University) ;
  • Wang, Peijun (Department of Mathematics Southeast University)
  • Received : 2013.01.08
  • Published : 2014.03.31
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Abstract

In this note, we generalize the weak maximum principle in [4] to the case of complete linear Weingarten hypersurface in Riemannian space form $\mathbb{M}^{n+1}(c)$ (c = 1, 0,-1), and apply it to estimate the norm of the total umbilicity tensor. Furthermore, we will study the linear Weingarten hypersurface in $\mathbb{S}^{n+1}(1)$ with the aid of this weak maximum principle and extend the rigidity results in Li, Suh, Wei [13] and Shu [15] to the case of complete hypersurface.

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References

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  2. Rigidity of linear Weingarten hypersurfaces in locally symmetric manifolds vol.289, pp.11-12, 2016, https://doi.org/10.1002/mana.201400296
  3. Linear Weingarten submanifolds in unit sphere vol.106, pp.6, 2016, https://doi.org/10.1007/s00013-016-0881-7