Clairaut surfaces in Euclidean three-space


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.

Tohoku Math. J.
Elena (Xinyi) Wang
Elena (Xinyi) Wang
PhD Student at CMSE

My research interests include topological data analysis(TDA), computational topology and geometry, and machine learning.