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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Tohoku Mathematical Journal. Second Series
( Vol. 55 NO.4 / (2003))
Hamiltonian Stability of Certain Minimal Lagrangian Submanifolds in Complex Projective Spaces
Amartuvshin Amarzaya, Yoshihiro Ohnita,
Pages. 583-610
Abstract A compact minimal Lagrangian submanifold immersed in a Kahler manifold is called Hamiltonian stable if the second variation of its volume is nonnegative under all Hamiltonian deformations. We study compact Hamiltonian stable minimal Lagrangian submanifolds with paralel second fundamental form embedded in complex projective spaces. Moreover, we completely determine Hamiltonian stability of all real forms in compact irreducible Hermitian symmetric spaces, which were classified previously by M.Takeuchi.
Contents 0. introduction
1. Hamiltonian stability of minimal Lagrangian submanifolds in Kahler manifolds.
2. Minimal Lagrangian submanifolds in $CP^n$ with parallel second fundamental form
3. Calculation of the first eigenvalues of minimal Lagrangian submanifold in $CP^n$ with parallel second fundamental form
4. Hamiltonian stability of minimal Lagrangian submanifolds in $CP^n$ with parallel second fundamental form.
5. Hamiltonian stability of symmetric $R$-spaces canonically embedded in Hermitian symmetric spaces.
Key words Lagrangian submanifold, minimal submanifold, Hamiltonian stability, symplectic geometry
Mathmatical Subject Classification 53C42, 53C40, 58G25