Self-intersections of Closed Parametrized Minimal Surfaces in Generic\n Riemannian Manifolds

2020/09/11 by John Douglas Moore, Moore, John Douglas
Computer Science · Mathematics · #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2009.05555

openalex publication_date 2020/09/11 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

This article shows that for generic choice of Riemannian metric on a smooth\nmanifold M of dimension four, all prime compact parametrized minimal surfaces\nwithin M have self-intersections in general position in the following sense:\nself-intersections are transverse and the two tangent planes at any\nself-intersection point fail to be complex with respect to any orthogonal\ncomplex structure on the ambient manifold M. This implies via a result of\nSheldon Chang that H₂(M; mathbb Z) is generated by homology classes that\nare represented by imbedded minimal surfaces.\n

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