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arXiv · 1711.05427

Application of a unified Kenmotsu-type formula for surfaces in Euclidean or Lorentzian three-space

Masatoshi Kokubu
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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.

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Masatoshi Kokubu. 2017-11-15. Application of a unified Kenmotsu-type formula for surfaces in Euclidean or Lorentzian three-space. https://arxiv.org/abs/1711.05427

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