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Weierstrass representation for timelike minimal surfaces in Minkowski 3-space

Sungwook Lee
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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.

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Sungwook Lee. 2006-08-30. Weierstrass representation for timelike minimal surfaces in Minkowski 3-space. https://arxiv.org/abs/math/0608726

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