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arXiv · 1704.05553

Hamiltonian stationary cones with isotropic links

Jingyi Chen·Yu Yuan
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Abstract

We show that any closed oriented immersed Hamiltonian stationary isotropic surface $\Sigma$ with genus $g_{\Sigma}$ in $S^{5}\subset\mathbb{C}^{3}$ is (1) Legendrian and minimal if $g_{\Sigma}=0$; (2) either Legendrian or with exactly $2g_{\Sigma}-2$ Legendrian points if $g_{\Sigma}\geq1.$ In general, every compact oriented immersed isotropic submanifold $L^{n-1}\subset S^{2n-1}\subset\mathbb{C}^{n}$ such that the cone $C\left( L^{n-1}\right) $ is Hamiltonian stationary must be Legendrian and minimal if its first Betti number is zero. Corresponding results for non-orientable links are also provided.

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Jingyi Chen, Yu Yuan. 2017-04-18. Hamiltonian stationary cones with isotropic links. https://doi.org/10.2140/pjm.2018.295.317

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