Open Access
April, 2020 On Hamiltonian stable Lagrangian tori in complex hyperbolic spaces
Toru KAJIGAYA
J. Math. Soc. Japan 72(2): 435-463 (April, 2020). DOI: 10.2969/jmsj/81158115

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 n2 and there exist infinitely many H-unstable Tn-orbits when n3. 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 n3 as well as the case of Cn and CPn.

Funding Statement

This work was supported by JSPS KAKENHI Grant Number JP18K13420.

Citation

Download Citation

Toru KAJIGAYA. "On Hamiltonian stable Lagrangian tori in complex hyperbolic spaces." J. Math. Soc. Japan 72 (2) 435 - 463, April, 2020. https://doi.org/10.2969/jmsj/81158115

Information

Received: 23 August 2018; Published: April, 2020
First available in Project Euclid: 5 February 2020

zbMATH: 07196909
MathSciNet: MR4090343
Digital Object Identifier: 10.2969/jmsj/81158115

Subjects:
Primary: 53D12
Secondary: 53C42

Keywords: complex hyperbolic spaces , Hamiltonian stable Lagrangian submanifolds

Rights: Copyright © 2020 Mathematical Society of Japan

Vol.72 • No. 2 • April, 2020
Back to Top