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Hamiltonian stability of Lagrangian tori in toric Kähler manifolds

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Let (M,J,ω) be a compact toric Kähler manifold of dim M=n and L a regular orbit of the T n-action on M. In the present paper, we investigate Hamiltonian stability of L, which was introduced by Y.-G. Oh (Invent. Math. 101, 501–519 (1990); Math. Z. 212, 175–192) (1993)). As a result, we prove any regular orbit is Hamiltonian stable when (M,ω)=ℂℙnFS) and (M,ω)=ℂℙn 1× ℂℙn 2,aωFS⊕ bωFS), where ωFS is the Fubini–Study Kähler form and a and b are positive constants. Moreover, they are locally Hamiltonian volume minimizing Lagrangian submanifolds.

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References

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Correspondence to Hajime Ono.

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Mathematics subject classifications (2000): 53C42, 53D12

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Ono, H. Hamiltonian stability of Lagrangian tori in toric Kähler manifolds. Ann Glob Anal Geom 31, 329–343 (2007). https://doi.org/10.1007/s10455-006-9037-5

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  • DOI: https://doi.org/10.1007/s10455-006-9037-5

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