[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2021.34.4.379

ON MINIMAL SURFACES WITH GAUSSIAN CURVATURE OF BIANCHI SURFACE TYPE

Min, Sung-Hong (Department of Mathematics Chungnam National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.34, no.4, 2021 , pp. 379-385 More about this Journal

Abstract

We consider the local uniqueness of a catenoid under the condition for the Gaussian curvature analogous to Bianchi surfaces. More precisely, if a nonplanar minimal surface in ℝ³ has the Gaussian curvature $K={\frac{1}{(U(u)+V(v))^2}}$ for any functions U(u) and V (v) with respect to a line of curvature coordinate system (u, v), then it is part of a catenoid. To do this, we use the relation between a conformal line of curvature coordinate system and a Chebyshev coordinate system.

Keywords

catenoid; Gaussian curvature; Chebyshev coordinate system; conjugate minimal surface;

Citations & Related Records

Reference

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