Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON MINIMAL SURFACES WITH GAUSSIAN CURVATURE OF BIANCHI SURFACE TYPE

  • Min, Sung-Hong (Department of Mathematics Chungnam National University)
  • Received : 2021.08.20
  • Accepted : 2021.10.20
  • Published : 2021.11.15
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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.

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References

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