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Let $R^{1,2}$ be the Minkowski 3-space, I would like to know any references about minimal (maximal) orientable Lorentzian surfaces in $\mathbb{R}^{1,2}$, including examples and maybe general theories, say something like Weierstrass representation. Here by minimal (maximal) I simply mean that the Lorentzian surface, as a submanifold of $\mathbb{R}^{1,2}$, has mean curvature 0.

Grazie!

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    $\begingroup$ The names that come to mind are Lopez and Ros; it has been a while. ugr.es/~aros $\endgroup$ Commented Jan 5, 2015 at 19:11

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These two books might be useful:

http://books.google.be/books/about/An_Introduction_to_Lorentz_Surfaces.html?id=1S_YJ39DSdcC&redir_esc=y

http://www.worldscientific.com/worldscibooks/10.1142/7542

(the Weierstrass representation is treated in detail in the second one)

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Think we have a winner:

http://www.ugr.es/~fjlopez/_private/rilo.pdf

I believe I was thinking of Rafael Lopez; I think he and Ros published things commenting on my dissertation, or similar to it anyway.

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  • $\begingroup$ Thanks for your reference! But it seems that the maximal surfaces he considered in this paper are Riemannian instead of Lorentzian. $\endgroup$ Commented Jan 5, 2015 at 19:21
  • $\begingroup$ @Piojo, quite possible. Meanwhile, I am having trouble finding a web page for the Granada Department of Geometry and Topology, which is clearly separate from the Department of Applied Mathematics that I found. $\endgroup$ Commented Jan 5, 2015 at 19:25

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