Ruled Lagrangian Submanifolds of the 6-Sphere
Ruled Lagrangian Submanifolds of the 6-Sphere
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DOI：
10.1090/s0002-9947-2010-05167-0
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发表时间：
2008-07
影响因子：
1.3
通讯作者：
Jason D. Lotay
中科院分区：
文献类型：
--
作者：
Jason D. Lotay
本文旨在达到双重目的。一方面，我们用“魏尔斯特拉斯公式”给出了由等半径圆支配的近Kahler 6球s6中的拉格朗日量的显式描述。另一方面，我们承认所有已知的拉格朗日函数的例子都被这样的圆所支配。因此，我们描述了s6中所有二阶基本形式满足自然点态条件的拉格朗日族，即所谓的二阶族。
This article sets out to serve a dual purpose. On the one hand, we give an explicit description of the Lagrangians in the nearly Kahler 6-sphere S 6 which are ruled by circles of constant radius using 'Weierstrass formulae'. On the other, we recognise all known examples of these Lagrangians as being ruled by such circles. Therefore, we describe all families of Lagrangians in S 6 whose second fundamental form satisfies natural pointwise conditions: so-called 'second order families'.