|
|
| |
| Conjugate Surfaces of a Family of Minimal Surfaces of Genus 1 with 4Planar Ends in R3 |
| |
Citation： |
Yulin SHI,Peng WANG,Xiaozhen WANG.Conjugate Surfaces of a Family of Minimal Surfaces of Genus 1 with 4Planar Ends in R3[J].Chinese Annals of Mathematics B,2024,45(6):927~942 |
| Page view： 422
Net amount： 156 |
Authors： |
Yulin SHI; Peng WANG;Xiaozhen WANG |
Foundation： |
the National Natural Science Foundation of China (Nos. 12371052,
11971107) and the National Natural Science Foundation of Fujian Province (Nos. 2023J01536,
2022J02028, 2021J05035). |
|
|
| Abstract： |
Costa first constructed a family of complete minimal surfaces which have genus
1 and 4 planar ends by use of Weierstrass-? functions. They are Willmore tori of Willmore
energy 16π. In this paper, the authors consider the geometry of conjugate surfaces of these
surfaces. It turns out that these conjugate surfaces are doubly periodic minimal surfaces
with flat ends in R3. Moreover, the authors can also perform a Lorentzian deformation
on these Costa’s minimal tori, which produce a family of complete space-like stationary
surfaces (i.e., of zero mean curvature) with genus 1 and 4 planar ends in 4-dimensional
Lorentz-Minkowski space R4 1. |
Keywords： |
Conjugate surfaces, Weierstrass representation, Elliptic functions,
Doubly periodic minimal surfaces |
Classification： |
53A10, 53C50, 53C42, 33E05 |
|
|
Download PDF Full-Text
|
|
|
|
