Deformations of isotropic submanifolds in Kähler manifolds

DOI10.1016/0393-0440(94)90061-2zbMath0788.53051OpenAlexW1994881304MaRDI QIDQ1317920

Bang-Yen Chen, Jean-Marie Morvan

Publication date: 12 June 1994

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(94)90061-2

zbMATH Keywords

minimal submanifoldsvariationsisotropic submanifoldsMaslov class

Mathematics Subject Classification ID

Global submanifolds (53C40) Local differential geometry of Hermitian and Kählerian structures (53B35)

Related Items (13)

Isoparametric surfaces and the \(\mathrm{tt}^\ast\)-equations ⋮ Hamiltonian stationary Lagrangian surfaces in \(\mathbb C \mathbb{P}^{2}\) ⋮ Hamiltonian minimality and Hamiltonian stability of Gauss maps ⋮ On anti-invariant Riemannian submersions whose total manifolds are locally product Riemannian ⋮ The Stability Problem of Certain Anti-Invariant Submanifolds in Golden Riemannian Manifolds ⋮ On Hamiltonian minimality of isotropic non-homogeneous tori in $\mathbb{H}^n$ and $\mathbb{C} \mathrm{P}^{2n+1}$ ⋮ On Hamiltonian-minimal isotropic homogeneous tori in \(\mathbb{C}^n\) and \(\mathbb{C}P^n\) ⋮ Hamiltonian stationary cones with isotropic links ⋮ The spectral data for Hamiltonian stationary Lagrangian tori in \(\mathbb R^4\) ⋮ Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori ⋮ Calibrations and Lagrangian submanifolds in the six sphere ⋮ Semi-invariant submersions whose total manifolds are locally product Riemannian ⋮ Maslov form and \(J\)-volume of totally real immersions.

Cites Work

• Stability of certain minimal submanifolds of compact Hermitian symmetric spaces
• Calibrated geometries
• Symplectic geometry and secondary characteristic classes
• Géométrie des surfaces lagrangiennes de \(C^ 2\). (Geometry of Lagrangean surfaces of \(C^ 2)\)
• Volume minimization of Lagrangian submanifolds under Hamiltonian deformations
• Sur l'algèbre des automorphismes infinitesimaux d'une variété symplectique
• On stable currents and their application to global problems in real and complex geometry
• Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds
• On Totally Real Submanifolds
• On an Integral Formula of Gauss-Bonnet-Grotemeyer
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