Classification of Lagrangian submanifolds in complex space forms satisfying a basic equality involving \(\delta(2,2)\)

DOI10.1016/J.DIFGEO.2011.11.008zbMath1237.53045OpenAlexW1983085724WikidataQ115356746 ScholiaQ115356746MaRDI QIDQ763059

Alicia Prieto-Martín, Bang-Yen Chen

Publication date: 8 March 2012

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2011.11.008

zbMATH Keywords

Lagrangian submanifoldoptimal inequalitiesChen invariants\(\delta \)-invariants\(\delta \)(22)-ideal immersion

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Global submanifolds (53C40) Optimization of shapes other than minimal surfaces (49Q10) Lagrangian submanifolds; Maslov index (53D12)

Related Items (6)

Complete Lagrangian ideal 𝛿(2) submanifolds in the complex projective space ⋮ Curvature inequalities for Lagrangian submanifolds: the final solution ⋮ \(\delta^{\sharp}(2,2)\)-ideal centroaffine hypersurfaces of dimension 4 ⋮ Remarks on Chen's inequalities for submanifolds of a Riemannian manifold of nearly quasi-constant curvature ⋮ \(\delta^{\sharp}(2,2)\)-ideal centroaffine hypersurfaces of dimension 5 ⋮ Lagrangian submanifolds in complex space forms satisfying equality in the optimal inequality involving \(\delta (2, \ldots, 2)\)

Cites Work

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• Some pinching and classification theorems for minimal submanifolds
• The imbedding problem for Riemannian manifolds
• Eine innere Kennzeichnung der verzerrten Produkte
• Intrinsic and extrinsic structures of Lagrangian surfaces in complex space forms
• Totally real submanifolds of \(\mathbb{C} P^ n\) satisfying a basic equality
• Lagrangian submanifolds attaining equality in the improved Chen's inequality
• Isometric immersions of Riemannian products
• $\delta$-Invariants, Inequalities of Submanifolds and Their Applications
• Ideal Lagrangian immersions in complex space forms
• On Totally Real Submanifolds
• An exotic totally real minimal immersion of S³ in ℂP³ and its characterisation

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