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Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds. (English) Zbl 0721.53060
Let M be a Kähler manifold, \(C_ 1(M)\) be the first Chern class and L be a minimal Lagrangian submanifold of M. First, by using a second variation formula, the author proves: a) If \(C_ 1(M)\leq 0\), then L is stable. b) If \(C_ 1(M)>0\), and L is stable then \(H^ 1(L,{\mathbb{R}})=\{0\}\). Then, in case M is an Einstein-Kähler manifold, he defines both local and global Hamiltonian stability of L. Finally he finds a general criterion of the local Hamiltonian stability and shows that such a criterion is satisfied by several minimal Lagrangian submanifolds.
Reviewer: A.Bejancu (Iaşi)

MSC:
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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