Weierstrass representation for timelike minimal surfaces in Minkowski 3-space
Differential Geometry
2007-05-23 v2
Abstract
Using techniques of integrable systems, we study a Weierstrass representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in Minkowski 3-space. The relationship between timelike minimal surfaces and bosonic Nambu-Goto string worldsheets in spacetime is also discussed in the appendix.
Cite
@article{arxiv.math/0608726,
title = {Weierstrass representation for timelike minimal surfaces in Minkowski 3-space},
author = {Sungwook Lee},
journal= {arXiv preprint arXiv:math/0608726},
year = {2007}
}
Comments
16 pages, 8 figures