Helicoidal surfaces with prescribed curvatures in a conformally flat 3-space
- Lee, Chul Woo; Lee, Jae Won; Yoon, Dae Won
- Issue Date
- WALTER DE GRUYTER GMBH
- Conformally flat space; helicoidal surface; extrinsic curvature; mean curvature
- GEORGIAN MATHEMATICAL JOURNAL, v.28, no.5, pp.755 - 763
- Journal Title
- GEORGIAN MATHEMATICAL JOURNAL
- Start Page
- End Page
- In this paper, we study a conformally flat 3-space. F-3 which is an Euclidean 3-space with a conformally flat metric with the conformal factor 1/F-2, where F(x) = e(-x12-x22) for x = (x(1), x(2), x(3)) is an element of R-3. In particular, we construct all helicoidal surfaces in F-3 by solving the second-order non-linear ODE with extrinsic curvature and mean curvature functions. As a result, we give classification of minimal helicoidal surfaces as well as examples for helicoidal surfaces with some extrinsic curvature and mean curvature functions in F-3.
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