Tohoku Mathematical Journal
2003
December
SECOND SERIES VOL. 55, NO. 4

Tohoku Math. J.
55 (2003), 583-610

Title HAMILTONIAN STABILITY OF CERTAIN MINIMAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX PROJECTIVE SPACES

Dedicated to Professor Koichi Ogiue on his sixtieth birthday
Author Amartuvshin Amarzaya and Yoshihiro Ohnita

(Received February 20, 2002, revised November 15, 2002)
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 parallel 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.

2000 Mathematics Subject Classification. Primary 53C42; Secondary 53C40, 58G25.
Key words and phrases. Lagrangian submanifold, minimal submanifold, Hamiltonian stability, symplectic geometry.

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