Classification of Lagrangian Surfaces of Curvature e in Non-flat Lorentzian Complex Space Form M12(4ε) |
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作者姓名: | Bang Yen CHEN |
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作者单位: | Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027, USA |
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摘 要: | It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12(4ε) of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is "Besides totally geodesic ones how many Lagrangian surfaces of constant curvature εin M12(46) are there?" In an earlier paper an answer to this question was obtained for the case e = 0 by Chen and Fastenakels. In this paper we provide the answer to this question for the case ε≠0. Our main result states that there exist thirty-five families of Lagrangian surfaces of curvature ε in M12(4ε) with ε ≠ 0. Conversely, every Lagrangian surface of curvature ε≠0 in M12(4ε) is locally congruent to one of the Lagrangian surfaces given by the thirty-five families.
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关 键 词: | 拉格朗日 常曲率 M12 洛伦兹 空间形式 位置 曲面 分类 |
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