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Abstract In this paper, we will prove that any closed minimal Willmore hypersurface M 4 of S 5 with constant scalar curvature must be isoparametric. To be precise, M 4… Click to show full abstract
Abstract In this paper, we will prove that any closed minimal Willmore hypersurface M 4 of S 5 with constant scalar curvature must be isoparametric. To be precise, M 4 is either an equatorial 4 sphere, a product of sphere S 2 ( 2 2 ) × S 2 ( 2 2 ) or a Cartan's minimal hypersurface. In particular, the value of the second fundamental form S can only be 0, 4, 12. This result strongly supports Chern's Conjecture.
Keywords:
minimal hypersurfaces;
constant scalar;
willmore minimal;
scalar curvature;
closed willmore
Journal Title: Advances in Mathematics
Year Published: 2017
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Journal Title: Advances in Mathematics
Year Published: 2017
Link to full text (if available)
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recommendations!