Classification of spherical Lagrangian submanifolds in complex Euclidean spaces

2013/08/25 by Bang‐Yen Chen, Chen, Bang-Yen
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1308.5366

openalex publication_date 2013/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An isometric immersion f:Mⁿ→ Mⁿ from a Riemannian n-manifold Mⁿ into a Kähler n-manifold Mⁿ is called \it Lagrangian if the complex structure J of the ambient manifold Mⁿ interchanges each tangent space of Mⁿ with the corresponding normal space. In this paper, we completely classify spherical Lagrangian submanifolds in complex Euclidean spaces. Furthermore, we also provide two corresponding classification theorems for Lagrangian submanifolds in the complex pseudo-Euclidean spaces with arbitrary complex index.

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