Hamiltonian stationary cones with isotropic links

Jingyi Chen, Yu Yuan
2018 Pacific Journal of Mathematics  
We show that any closed oriented immersed Hamiltonian stationary isotropic surface Σ with genus g_Σ in S^5⊂C^3 is (1) Legendrian and minimal if g_Σ=0; (2) either Legendrian or with exactly 2g_Σ-2 Legendrian points if g_Σ≥1. In general, every compact oriented immersed isotropic submanifold L^n-1⊂ S^2n-1⊂C^n such that the cone C( L^n-1) is Hamiltonian stationary must be Legendrian and minimal if its first Betti number is zero. Corresponding results for non-orientable links are also provided.
doi:10.2140/pjm.2018.295.317 fatcat:owtery223fhmhji2piomigwggm