Geodesics of positive Lagrangians in Milnor fibers
Geodesics of positive Lagrangians in Milnor fibers
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Milnor 纤维中正拉格朗日测地线
DOI：
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发表时间：
2015
期刊：
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通讯作者：
Amitai M. Yuval
中科院分区：
文献类型：
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作者：
Jake Solomon;Amitai M. Yuval
几乎卡-丘流形中的正拉格朗日空间是所有拉格朗日子流形空间中的开集。一个哈密顿合痕类的正拉格朗日承认一个自然的黎曼度量$Uppermian $，这引起了一个概念的测地线。研究了n维Milnor纤维中正的O_n（mathbb{R}）$不变拉格朗日球面的测地线.我们证明了初值问题和边值问题光滑解的存在唯一性。特别地，我们得到了任意维正拉格朗日量的光滑测地线的例子。作为应用，我们证明了在上述Milnor纤维中，黎曼度量$Uppermian $在正的$O_n（mathbb{R}）$不变拉格朗日球面空间上诱导出一个度量空间结构.
The space of positive Lagrangians in an almost Calabi-Yau manifold is an open set in the space of all Lagrangian submanifolds. A Hamiltonian isotopy class of positive Lagrangians admits a natural Riemannian metric $Upsilon$, which gives rise to a notion of geodesics. We study geodesics of positive $O_n(mathbb{R})$ invariant Lagrangian spheres in $n$-dimensional $A_m$ Milnor fibers. We show the existence and uniqueness of smooth solutions to the initial value problem and the boundary value problem. In particular, we obtain examples of smooth geodesics of positive Lagrangians in arbitrary dimension. As an application, we show that the Riemannian metric $Upsilon$ induces a metric space structure on the space of positive $O_n(mathbb{R})$ invariant Lagrangian spheres in the above mentioned Milnor fibers.