open access

https://hdl.handle.net/2115/81689

Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space

英語

Tzitzeica equations

2020-06-05

Springer

Annali di matematica pura ed applicata

200(2)

521-546

It has been known for some time that there exist 5 essentially different real forms of the complex affine Kac-Moody algebra of type A(2)((2)) and that one can associate 4 of these real forms with certain classes of "integrable surfaces," such as minimal Lagrangian surfaces in CP2 and CH2, as well as definite and indefinite affine spheres in R-3. In this paper, we consider the class of timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space CH12. We show that this class of surfaces corresponds to the fifth real form. Moreover, for each timelike Lagrangian surface in CH12 we define natural Gauss maps into certain homogeneous spaces and prove a Ruh-Vilms-type theorem, characterizing timelike minimal Lagrangian surfaces among all timelike Lagrangian surfaces in terms of the harmonicity of these Gauss maps.

学術雑誌論文

Accepted Manuscript

This is a post-peer-review, pre-copyedit version of an article published in Annali di Matematica Pura ed Applicata. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10231-020-01005-1

0373-3114