Index of Lagrangian submanifolds of \(\mathbb{C} \mathbb{P}^ n\) and the Laplacian of 1-forms

DOI10.1007/BF01264074zbMath0802.53013OpenAlexW1967320832MaRDI QIDQ1312324

Francisco Urbano

Publication date: 11 December 1994

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01264074

zbMATH Keywords

LaplacianLagrangian immersiontotally geodesic embeddingtotally geodesic immersionFubini Study metricgeneralized Clifford torus

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20)

Related Items (9)

Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces ⋮ The geometric complexity of special Lagrangian \(T^2\)-cones ⋮ Almost all Lagrangian torus orbits in \(\mathbb CP^n\) are not Hamiltonian volume minimizing ⋮ Lifting Lagrangian immersions in \(\mathbb{C}P^{n-1}\) to Lagrangian cones in \(\mathbb{C}^n\) ⋮ On stable compact minimal submanifolds of Riemannian product manifolds ⋮ Second variation of compact minimal Legendrian submanifolds of the sphere ⋮ Spin\(^{c}\) geometry of Kähler manifolds and the Hodge Laplacian on minimal Lagrangian sub\-manifolds ⋮ Calibrations and Lagrangian submanifolds in the six sphere ⋮ On Hamiltonian stable minimal Lagrangian surfaces in \({\mathbb{C}}\text{P}^2\)

Cites Work

• Unnamed Item
• On spectral geometry of Kähler submanifolds
• Totally real submanifolds and symmetric bounded domains
• Curvature pinching and eigenvalue rigidity for minimal submanifolds
• Stability of harmonic maps and standard minimal immersions
• On stable currents and their application to global problems in real and complex geometry
• Minimal varieties in Riemannian manifolds
• Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds
• Submanifolds with Constant Mean Curvature

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