Spheres and Tori as Elliptic Linear Weingarten Surfaces

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Abstract
The linear Weingarten condition with ellipticity for the mean curvature and the extrinsic Gaussian curvature on a surface in the three-sphere can define a Riemannian metric which is called the elliptic linear Weingarten metric. We established some local characterizations of the round spheres and the tori immersed in the 3-dimensional unit sphere, along with the Laplace operator, the spherical Gauss map and the Gauss map associated with the elliptic linear Weingarten metric.
Funding Information
  • National Research Foundation of Korea (2018R1D1A3B05050223, 2020R1I1A3051852)
  • National Natural Science Foundation of China (11801065)
  • Fundamental Research Funds for the Central Universities (N2005012)

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