On Hamiltonian stable Lagrangian tori in complex hyperbolic spaces

2018/08/23 by Kajigaya, Toru
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.07745

Abstract

In this paper, we investigate the Hamiltonian-stability of Lagrangian tori in the complex hyperbolic space ℂHⁿ. We consider a standard Hamiltonian Tⁿ-action on ℂHⁿ, and show that every Lagrangian Tⁿ-orbits in ℂHⁿ is H-stable when n≤ 2 and there exist infinitely many H-unstable Tⁿ-orbits when n≥ 3. On the other hand, we prove a monotone Tⁿ-orbit in ℂHⁿ is H-stable and rigid for any n. Moreover, we see almost all Lagrangian Tⁿ-orbits in ℂHⁿ are not Hamiltonian volume minimizing when n≥ 3 as well as the case of ℂⁿ and ℂPⁿ.

Related

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• Almost all standard Lagrangian tori in Cⁿ are not Hamiltonian volume minimizing
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• Hamiltonian stationary Lagrangian tori contained in a hypersphere
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