A rigidity theorem for hypersurfaces of the odd-dimensional unit sphere
Tom 174 / 2023
Colloquium Mathematicum 174 (2023), 151-160
MSC: Primary 53C24; Secondary 53C25, 53C40.
DOI: 10.4064/cm8966-7-2023
Opublikowany online: 9 October 2023
Streszczenie
We establish an optimal integral inequality for closed hypersurfaces in the odd-dimensional unit sphere \mathbb S^{2n+1}(1) with vanishing Reeb function that involves the shape operator A and the contact vector field U. The integral inequality is optimal in that all hypersurfaces attaining the equality are determined. Moreover, we obtain a new characterization for the Clifford hypersurfaces \mathbb S^{2p+1}(r_1)\times \mathbb S^{2q+1}(r_2) in \mathbb S^{2n+1}(1) with p+q=n-1 and r_1^2+r_2^2=1.
