# Elliptic Linear Weingarten Surfaces

• Kim, Young Ho (Department of Mathematics, Kyungpook National University)
• Accepted : 2018.05.25
• Published : 2018.09.23
• 116 8

#### Abstract

We establish some characterizations of isoparametric surfaces in the three-dimensional Euclidean space, which are associated with the Laplacian operator defined by the so-called II-metric on surfaces with non-degenerate second fundamental form and the elliptic linear Weingarten metric on surfaces in the three-dimensional Euclidean space. We also study a Ricci soliton associated with the elliptic linear Weingarten metric.

#### Keywords

elliptic linear Weingarten metric;finite-type immersion;Gauss map;isoparametric surface;Ricci soliton

#### References

1. B.-Y. Chen, Linearly independent, orthogonal and equivariant immersions, Kodai Math. J., 14(1991), 341-349. https://doi.org/10.2996/kmj/1138039459
2. B.-Y. Chen, Total mean curvature and submanifolds of finite type, Second edition, World Scientific, Hackensack, NJ, 2015.
3. J. A. Galvez, A. Martinez and F. Milan, Linear Weingarten surfaces in $R^3$, Monatsh. Math., 138(2003), 133-144.
4. H. Hopf, Differential Geometry in the Large, Lecture Notes in Mathematics 1000, Springer-Verlag, Berlin, 1983.
5. D.-S. Kim, Y. H. Kim and D. W. Yoon, Characterizations of tori in 3-sphere, Tai-wanese J. Math., 20(2016), 1053-1064. https://doi.org/10.11650/tjm.20.2016.7247
6. T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan, 18(1966), 380-385. https://doi.org/10.2969/jmsj/01840380