2022 Clairaut surfaces in Euclidean three-space
Andrew D. Hwang, Xinyi Wang
Tohoku Math. J. (2) 74(2): 215-227 (2022). DOI: 10.2748/tmj.20201209

Abstract

In this note, we investigate local isometric immersion of Clairaut metrics in Euclidean three-space. A Clairaut metric is determined up to isometry by a single function of one variable. We show that an isometric immersion is formally determined by two functions of one variable, uniquely up to coordinate reflection and ambient Euclidean motions. Further, if the Clairaut metric and these two functions are real-analytic, there exists a local isometric immersion realizing these data. We give a more explicit description for a finite-dimensional family of examples.

Citation

Download Citation

Andrew D. Hwang. Xinyi Wang. "Clairaut surfaces in Euclidean three-space." Tohoku Math. J. (2) 74 (2) 215 - 227, 2022. https://doi.org/10.2748/tmj.20201209

Information

Published: 2022
First available in Project Euclid: 6 July 2022

MathSciNet: MR4455865
zbMATH: 1500.53006
Digital Object Identifier: 10.2748/tmj.20201209

Subjects:
Primary: 53A05
Secondary: 53B25 , 53D99

Keywords: Clairaut metric , isometric immersion , surfaces , symplectic for

Rights: Copyright © 2022 Tohoku University

Vol.74 • No. 2 • 2022
Back to Top