Contact stationary Legendrian surfaces in \(\mathbb S^5\)

DOI10.2140/pjm.2018.293.101zbMath1383.53048arXiv1211.4227OpenAlexW3106015994MaRDI QIDQ1679929

Yong Luo

Publication date: 22 November 2017

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.4227

zbMATH Keywords

contact manifoldSimons' inequalityvolume functionalgap theoremvariationLegendrian submanifold

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Local submanifolds (53B25)

Related Items

Sharp estimates for the first eigenvalue of Schrödinger operator in the unit sphere ⋮ An optimal inequality related to characterizations of the contact Whitney spheres in Sasakian space forms ⋮ On \(C\)-totally real submanifolds of \(\mathbb{S}^{2n+1}(1)\) with non-negative sectional curvature ⋮ On energy gap phenomena of the Whitney sphere and related problems ⋮ Some optimal inequalities for anti-invariant submanifolds of the unit sphere ⋮ Rigidity of closed CSL submanifolds in the unit sphere ⋮ Minimal Legendrian submanifolds in Sasakian space forms with \(C\)-parallel second fundamental form ⋮ \(C\)-totally real submanifolds with constant sectional curvature in the Sasakian space forms ⋮ Addendum to the article ``Contact stationary Legendrian surfaces in \(\mathbb{S}^5\) ⋮ On \(C\)-totally real minimal submanifolds of the Sasakian space forms with parallel Ricci tensor

Cites Work

• Construction of Lagrangian submanifolds in \(\mathbb C\mathbb P^n\)
• Hamiltonian stationary tori in Kähler manifolds
• The existence of Hamiltonian stationary Lagrangian tori in Kähler manifolds of any dimension
• Second variation and Legendrian stabilities of minimal Legendrian submanifolds in Sasakian manifolds
• The classification of Hamiltonian stationary Lagrangian tori in \({{\mathbb {CP}}^2}\) by their spectral data
• Willmore hypersurfaces in a sphere
• Spectral data for Hamiltonian-minimal Lagrangian tori in \(\mathbb CP^{2}\)
• Minimal immersions of 2-manifolds into spheres
• Some explicit examples of Hamiltonian minimal Lagrangian submanifolds in complex space forms
• Hamiltonian-minimal Lagrangian submanifolds in Kähler manifolds with symmetries
• Equivariant gluing constructions of contact stationary Legendrian submanifolds in \({\mathbb {S}^{2n+1}}\)
• C-totally real submanifolds of Sasakian space forms
• Analysis - 10
• Volume minimization of Lagrangian submanifolds under Hamiltonian deformations
• Willmore surfaces in \(S^n\)
• Minimizing area among Lagrangian surfaces: the mapping problem.
• Willmore submanifolds in a sphere.
• Closed Legendre geodesics in Sasaki manifolds
• A minimizing deformation of Legendrian submanifolds in the standard sphere
• Hamiltonian-minimal Lagrangian submanifolds in complex space forms
• Hamiltonian stationary Lagrangian surfaces in \(\mathbb C \mathbb{P}^{2}\)
• Second variation formula and the stability of Legendrian minimal submanifolds in Sasakian manifolds
• Examples of Hamiltonian stationary Lagrangian tori in \(\mathbb CP^2\)
• Local rigidity theorems for minimal hypersurfaces
• Minimal varieties in Riemannian manifolds
• Hamiltonian minimal Lagrangian cones in \(\mathbb C^m\)
• Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds
• On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds
• Submanifolds with Constant Mean Curvature
• A Totally Real Surface in CP 2 that is not Totally Geodesic
• Hamiltonian stationary tori in the complex projective plane
• A Theorem on C-Totally Real Minimal Surface
• Special Lagrangian cones
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length