A compact minimal Lagrangian submanifold immersed in a Kähler 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.
@article{1113247132,
author = {Amarzaya, Amartuvshin and Ohnita, Yoshihiro},
title = {Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces},
journal = {Tohoku Math. J. (2)},
volume = {55},
number = {2},
year = {2003},
pages = { 583-610},
language = {en},
url = {http://dml.mathdoc.fr/item/1113247132}
}
Amarzaya, Amartuvshin; Ohnita, Yoshihiro. Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces. Tohoku Math. J. (2), Tome 55 (2003) no. 2, pp. 583-610. http://gdmltest.u-ga.fr/item/1113247132/