#### Vol. 295, No. 2, 2018

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Hamiltonian stationary cones with isotropic links

### Jingyi Chen and Yu Yuan

Vol. 295 (2018), No. 2, 317–327
##### Abstract

We show that any closed oriented immersed Hamiltonian stationary isotropic surface $\Sigma$ with genus ${g}_{\Sigma }$ in ${S}^{5}\subset {ℂ}^{3}$ is (1) Legendrian and minimal if ${g}_{\Sigma }=0$; (2) either Legendrian or with exactly $2{g}_{\Sigma }-2$ Legendrian points if ${g}_{\Sigma }\ge 1$. In general, every compact oriented immersed isotropic submanifold ${L}^{n-1}\subset {S}^{2n-1}\subset {ℂ}^{n}$ 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 nonorientable links are also provided.

 In memory of Professor Wei-Yue Ding

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