| Classification of Flat Lagrangian Surfaces in Complex Lorentzian Plane |
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| 引用本文： | Bang-Yen CHEN Johan FASTENAKELS. Classification of Flat Lagrangian Surfaces in Complex Lorentzian Plane[J]. 数学学报(英文版), 2007, 23(12): 2111-2144. DOI: 10.1007/s10114-007-0991-z |
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| 作者姓名： | Bang-Yen CHEN Johan FASTENAKELS |
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| 作者单位： | [1]Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA [2]Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium |
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| 基金项目： | A portion of this article was done while the second author visited Michigan State University, supported under a research grant for Research Assistant of the Fund for Scientific Research Flanders （Belgium） （FWO） |
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| 摘 要： |
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| 关 键 词： | 拉格朗日流形 复平面 勒让德曲线 黎曼几何 |
| 收稿时间： | 2005-12-02 |
| 修稿时间： | 2007-03-29 |
Classification of Flat Lagrangian Surfaces in Complex Lorentzian Plane |
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| Bang-Yen Chen,Johan Fastenakels. Classification of Flat Lagrangian Surfaces in Complex Lorentzian Plane[J]. Acta Mathematica Sinica(English Series), 2007, 23(12): 2111-2144. DOI: 10.1007/s10114-007-0991-z |
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| Authors: | Bang-Yen Chen Johan Fastenakels |
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| Affiliation: | (1) Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA;(2) Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium |
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| Abstract: | One of the most fundamental problems in the study of Lagrangian submanifolds from Riemannian geometric point of view is to classify Lagrangian immersions of real space forms into complex space forms. The main purpose of this paper is thus to classify flat Lagrangian surfaces in the Lorentzian complex plane C1^2. Our main result states that there are thirty-eight families of flat Lagrangian surfaces in C1^2. Conversely, every flat Lagrangian surface in C1^2 is locally congruent to one of the thirty-eight families. |
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| Keywords: | flat Lagrangian surfaces Lorentzian complex plane Legendre curve |
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