复曲面簇中的Hamilton极小拉格朗日子流形
Hamiltonian minimal Lagrangian submanifolds in toric varieties
摘要：
拉格朗日子流形的Hamilton极小性（H-极小性）是黎曼极小性的一个辛模拟。一个拉格朗日子流形称为H-极小子流形，如果它的体积沿所有哈密顿向量场的变化为零.这个概念是在Y. G.这与著名的关于哈密顿辛同胚的不动点个数的Arnold猜想有关。在以前的工作中，作者定义并研究了复空间中由Hermitian二次曲面的交所产生的一类H-极小拉格朗日子流形。在这里，我们将这个结构推广到定义H-极小子流形在环面品种。
英文摘要：
Hamiltonian minimality (H-minimality) for Lagrangian submanifolds is a symplectic analogue of Riemannian minimality. A Lagrangian submanifold is called H-minimal if the variations of its volume along all Hamiltonian vector fields are zero. This notion was introduced in the work of Y.-G. Oh in connection with the celebrated Arnold conjecture on the number of fixed points of a Hamiltonian symplectomorphism. In the previous works the authors defined and studied a family of H-minimal Lagrangian submanifolds in complex space arising from intersections of Hermitian quadrics. Here we extend this construction to define H-minimal submanifolds in toric varieties.
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