Complete parallel mean curvature surfaces in two-dimensional complex space-forms
Differential Geometry
2021-11-02 v2
Abstract
The purpose of this article is to determine explicitly the complete surfaces with parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. The main results are as follows: When the curvature of the ambient space is positive, there exists a unique such surface up to rigid motions of the target space. On the other hand, when the curvature of the ambient space is negative, there are `non-trivial' complete parallel mean curvature surfaces generated by Jacobi elliptic functions and they exhaust such surfaces.
Cite
@article{arxiv.1712.07757,
title = {Complete parallel mean curvature surfaces in two-dimensional complex space-forms},
author = {Katsuei Kenmotsu},
journal= {arXiv preprint arXiv:1712.07757},
year = {2021}
}
Comments
15pages, LaTex:typos added, to appear in Bull. Brazilian Math. Soc. (2018)