Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces

DOI10.2748/tmj/1113247132zbMath1062.53053OpenAlexW2061662476MaRDI QIDQ1876288

Amartuvshin Amarzaya, Yoshihiro Ohnita

Publication date: 16 August 2004

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1113247132

zbMATH Keywords

symplectic geometryLagrangian submanifoldsminimal submanifoldsHamiltonian stability

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Lagrangian submanifolds; Maslov index (53D12)

Related Items (17)

Reductions of minimal Lagrangian submanifolds with symmetries ⋮ On Hamiltonian stable Lagrangian tori in complex hyperbolic spaces ⋮ A monotone Lagrangian casebook ⋮ Hamiltonian-minimal Lagrangian submanifolds in Kähler manifolds with symmetries ⋮ Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces. II. ⋮ Symplectic topology of Lagrangian submanifolds of \(\mathbb{C}P^{n}\) with intermediate minimal Maslov numbers ⋮ Second variation formula and the stability of Legendrian minimal submanifolds in Sasakian manifolds ⋮ Construction of homogeneous Lagrangian submanifolds in \(\mathbb CP^n\) and Hamiltonian stability ⋮ The existence of Hamiltonian stationary Lagrangian tori in Kähler manifolds of any dimension ⋮ Hamiltonian-stationary Lagrangian surfaces of constant curvature \(\varepsilon \) in complex space form \(\tilde M ^2(4\varepsilon )\) ⋮ Classification of a family of Hamiltonian-stationary Lagrangian submanifolds in \(\mathbb C^{n}\) ⋮ Classification of Hamiltonian-stationary Lagrangian submanifolds of constant curvature in \(\mathbb CP^3\) with positive relative nullity ⋮ A class of non-compact homogeneous Lagrangian submanifolds in complex hyperbolic spaces ⋮ Warped product decompositions of real space forms and Hamiltonian-stationary Lagrangian submanifolds ⋮ On Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres ⋮ PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS INCPⁿ ⋮ Spectral geometry of the Jacobi operator of totally real submanifolds in \(Q\mathbb{P}^n\)

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