Spheres and Tori as Elliptic Linear Weingarten Surfaces

Dong-Soo Kim, Young Ho Kim () and Jinhua Qian
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Dong-Soo Kim: Department of Mathematics, Chonnam National University, Gwangju 61186, Korea
Young Ho Kim: Department of Mathematics, Kyngpook National University, Daegu 41566, Korea
Jinhua Qian: Department of Mathematics, Northeastern University, Shenyang 110004, China

Mathematics, 2022, vol. 10, issue 21, 1-8

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.

Keywords: elliptic linear Weingarten metric; finite-type immersion; spherical Gauss map; isoparametric surface; torus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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