【摘 要】
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Let SO(n) act in the standard way on Cn and extend this action in the usual way toCn+1=C((+))Cn.It is shown that a nonsingular special Lagrangian submanifold L
【机 构】
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Dedicated to the memory of Shiing-Shen Chern
【基金项目】
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Project supported by Duke University via a research grant;the NSF via DMS-0103884;the Mathematical Sciences Research Institute;Columbia University
论文部分内容阅读
Let SO(n) act in the standard way on Cn and extend this action in the usual way toCn+1=C((+))Cn.It is shown that a nonsingular special Lagrangian submanifold L (∩) Cn+1 that is invariant under this SO(n)-action intersects the fixed C (∩) Cn+1 in a nonsingular real-analytic arc A (which may be empty). If n ＞ 2, then A has no compact component.Conversely, an embedded, noncompact nonsingular real-analytic arc A (∩) C lies in an embedded nonsingular special Lagrangian submanifold that is SO(n)-invariant. The same existence result holds for compact A if n = 2. If A is connected, there exist n distinct nonsingular SO(n)-invariant special Lagrangian extensions of A such that any embedded nonsingular SO(n)-invariant special Lagrangian extension of A agrees with one of these n extensions in some open neighborhood of A.The method employed is an analysis of a singular nonlinear PDE and ultimately calls on the work of Gérard and Tahara to prove the existence of the extension.
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