A rigidity theorem of ξ-submanifolds in ℂ²

2015/11/09 by Xingxiao Li, Li, Xingxiao, Xiufen Chang +1
Mathematics · #Codimension #Compactness theorem #Curvature #Differential Geometry (math.DG) #FOS: Mathematics #Fundamental theorem #Generalization #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Lagrangian #Lambda #Mathematical analysis #Mathematics #Mean curvature #Mean curvature flow #Physics #Primary 53A30 #Pure mathematics #Quantum mechanics #Rigidity (electromagnetism) #Secondary 53B25 #Squeeze theorem #Submanifold #math.DG #msc:53A30 #msc:53B25

paper · pdf · doi:10.48550/arxiv.1511.02568

Submitted

arxiv created 2015/11/09 · openalex publication_date 2015/11/09 · arxiv updated 2015/11/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this paper, we first introduce the concept of ξ-submanifold which is a natural generalization of self-shrinkers for the mean curvature flow and also an extension of λ-hypersurfaces to the higher codimension. Then, as the main result, we prove a rigidity theorem for Lagrangian ξ-submanifold in the complex 2-plane \bbc².

Related

• The rigidity theorem for complete Lagrangian self-shrinkers
• Variational characterizations of ξ-submanifolds in the Eulicdean space \bbr^m+p
• Rigidity Theorems For Lagrangian Submanifolds of Cⁿ and CPⁿ With Conformal Maslov Form
• Rigidity theorems for constant weighted mean curvature hypersurfaces
• Mean curvature flow of surfaces in a hyperkähler 4-manifold