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Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space
| Title: | Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space |
| Authors: | Dorfmesiter, Josef F. Browse this author | | Kobayashi, Shimpei Browse this author |
| Keywords: | Timelike minimal Lagrangian surfaces | | Loop groups | | Real forms | | Tzitzeica equations |
| Issue Date: | 5-Jun-2020 |
| Publisher: | Springer |
| Journal Title: | Annali di matematica pura ed applicata |
| Volume: | 200 |
| Issue: | 2 |
| Start Page: | 521 |
| End Page: | 546 |
| Publisher DOI: | 10.1007/s10231-020-01005-1 |
| Abstract: | 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. |
| Rights: | 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 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/81689 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 小林 真平
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