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 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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Keywords
Hamiltonian stationary cone, minimal Legendrian link
Mathematical Subject Classification 2010
Primary: 58J05
Milestones
Received: 2 May 2017
Revised: 10 October 2017
Accepted: 9 January 2018
Published: 11 April 2018
Authors
Jingyi Chen
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada
Yu Yuan
Department of Mathematics
University of Washington
Seattle, WA
United States