A new obstruction to minimal isometric immersions into a real space form

2005/11/03 by Oprea, Teodor
Mathematics · #49K35 #53C21 #53C24 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Optimization and Control (math.OC) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.math/0511089

openalex publication_date 2005/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the theory of minimal submanifold, the following problem is fundamental: when does a given Riemannian manifold admit (or does not admit) a minimal isometric immersion into an Euclidean space form of arbitrary dimension? A partial solution of this problem was obtained by B.Y. Chen as an application of his fundamental inequality [1]. In this paper we obtain another partial solution of this problem.

Related

• Minimal immersions of Riemannian manifolds in products of space forms
• Minimal Kähler submanifolds in product of space forms
• Convexity, Rigidity, and Reduction of Codimension of Isometric Immersions into Space Forms
• Isotropic and Kähler Immersions
• Complete minimal submanifolds with nullity in Euclidean space