A new characterization of the Calabi torus in the unit sphere
Differential Geometry
2019-11-20 v1
Abstract
In this paper, we study the rigidity theorem of closed minimally immersed Legendrian submanifolds in the unit sphere. Utilizing the maximum principle, we obtain a new characterization of the Calabi torus in the unit sphere which is the minimal Calabi product Legendrian immersion of a point and the totally geodesic Legendrian sphere. We also establish an optimal Simons' type integral inequality in terms of the second fundamental form of three dimensional closed minimal Legendrian submanifolds in the unit sphere.
Keywords
Cite
@article{arxiv.1911.08155,
title = {A new characterization of the Calabi torus in the unit sphere},
author = {Yong Luo and Linlin Sun and Jiabin Yin},
journal= {arXiv preprint arXiv:1911.08155},
year = {2019}
}