Application of a unified Kenmotsu-type formula for surfaces in Euclidean or Lorentzian three-space
Differential Geometry
2017-11-16 v1
Abstract
Kenmotsu's formula describes surfaces in Euclidean 3-space by their mean curvature functions and Gauss maps. In Lorentzian 3-space, Akutagawa-Nishikawa's formula and Magid's formula are Kenmotsu-type formulas for spacelike surfaces and for timelike surfaces, respectively. We apply them to a few problems concerning rotational or helicoidal surfaces with constant mean curvature. Before that, we show that the three formulas above can be written in a unified single equation.
Keywords
Cite
@article{arxiv.1711.05427,
title = {Application of a unified Kenmotsu-type formula for surfaces in Euclidean or Lorentzian three-space},
author = {Masatoshi Kokubu},
journal= {arXiv preprint arXiv:1711.05427},
year = {2017}
}
Comments
27 pages, 13 figures