Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms
| dc.creator | Bryant, Robert L. | |
| dc.date | 1999-09-27 | |
| dc.date.accessioned | 2026-07-07T05:30:54Z | |
| dc.date.available | 2026-07-07T05:30:54Z | |
| dc.description | The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essentially unique example that is invariant under this one-parameter subgroup. On the other hand, when the curvature of the space form is zero, i.e., when the space form is complex 2-space with its standard flat metric, there is an additional `exceptional' example that has no continuous symmetries but is invariant under a lattice of translations. Up to isometry and homothety, this is the unique example with no continuous symmetries. | |
| dc.description | AMS-TeX 2.1, 35 pages, uses amsppt.sty | |
| dc.identifier | https://arxiv.org/abs/math/9909159 | |
| dc.identifier | http://arxiv.org/abs/math/9909159 | |
| dc.identifier | Adv. Stud. Pure Math., 37, Math. Soc. Japan, Tokyo, 2002, 1--44 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79155 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 32F25 (Primary), 53C42 (Secondary) | |
| dc.title | Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms | |
| dc.type | text |