On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms

DOI10.1007/S00013-016-0876-4zbMath1343.53057arXiv1412.0147OpenAlexW3102436054MaRDI QIDQ258061

Nikos Georgiou, Guillermo Antonio Lobos

Publication date: 17 March 2016

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.0147

zbMATH Keywords

Kähler structuresreal space formsHamiltonian minimal submanifoldsspace of oriented geodesics

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Lagrangian submanifolds; Maslov index (53D12) Non-Euclidean differential geometry (53A35)

Related Items (1)

A para-Kähler structure in the space of oriented geodesics in a real space form

Cites Work

• Hamiltonian stationary tori in Kähler manifolds
• The existence of Hamiltonian stationary Lagrangian tori in Kähler manifolds of any dimension
• Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface
• On the geometry of spaces of oriented geodesics
• On the space of oriented geodesics of hyperbolic 3-space
• Monopoles and geodesics
• Volume minimization of Lagrangian submanifolds under Hamiltonian deformations
• Buckling eigenvalues, Gauss maps and Lagrangian submanifolds
• On the geometry of the space of oriented lines of Euclidean space
• Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds
• On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds
• Spaces of geodesics of pseudo-Riemannian space forms and normal congruences of hypersurfaces
• An Indefinite Kähler Metric on the Space of Oriented Lines
• ON THE GEOMETRY OF THE SPACE OF ORIENTED LINES OF THE HYPERBOLIC SPACE

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