Minimal Lagrangian submanifolds with constant sectional curvature in indefinite complex space forms
Minimal Lagrangian submanifolds with constant sectional curvature in indefinite complex space forms
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DOI：
10.1090/s0002-9939-01-06213-x
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发表时间：
2001-10
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影响因子：
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通讯作者：
L. Vrancken
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文献类型：
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作者：
L. Vrancken
我们研究了不定实空间型Mn S(C)到不定复空间型Mn S(4c)的极小Lagrangian浸入。在c=c的条件下，我们证明了M n S(C)必是平坦的，并得到了浸没的一个显式刻画。在度量为正定或洛伦兹的情况下，这一结果分别由Ejiri(1982)和Kriele和作者(1999)得到。在c=c的情况下，这个定理不再成立；例如，参见陈和作者发现的例子(接受发表在东北数学杂志上)。
We study minimal Lagrangian immersions from an indefinite real space form M n s (c) into an indefinite complex space form M n s (4c). Provided that c ¬= c, we show that M n s (c) has to be flat and we obtain an explicit description of the immersion. In the case when the metric is positive definite or Lorentzian, this result was respectively obtained by Ejiri (1982) and by Kriele and the author (1999). In the case that c = c, this theorem is no longer true; see for instance the examples discovered by Chen and the author (accepted for publication in the Tohoku Mathematical Journal).