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Journal of University of Chinese Academy of Sciences ›› 2023, Vol. 40 ›› Issue (1): 6-11.DOI: 10.7523/j.ucas.2020.0058

• Research Articles • Previous Articles    

Bonnet surfaces with constant Gauss curvature

LI Miaomiao, WU Yingyi   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2020-08-20 Revised:2020-10-03

Abstract: A surfce in Euclidean 3-space $\mathbb{R}$3 is called Bonnet surface if it admits a nontrivial(not the restriction on a surface of rigid motions) one-parameter families of isometric immersions which preserve the mean curvature. Chen and Peng got the ODE of a Bonnet surface. Using this ODE, we give another proof of Colares-Kenmotsu theorem.

Key words: Bonnet surface, Gauss curvature, mean curvature

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