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

We show that any closed oriented immersed Hamiltonian stationary isotropic surface Σ with genus gΣ in S5 3 is (1) Legendrian and minimal if gΣ = 0; (2) either Legendrian or with exactly 2gΣ 2 Legendrian points if gΣ 1. In general, every compact oriented immersed isotropic submanifold Ln1 S2n1 n such that the cone C(Ln1) 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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Hamiltonian stationary cone, minimal Legendrian link
Mathematical Subject Classification 2010
Primary: 58J05
Received: 2 May 2017
Revised: 10 October 2017
Accepted: 9 January 2018
Published: 11 April 2018
Jingyi Chen
Department of Mathematics
University of British Columbia
Vancouver, BC
Yu Yuan
Department of Mathematics
University of Washington
Seattle, WA
United States