Classification of minimal Lorentz surfaces in indefinite space forms with arbitrary codimension and arbitrary index

2013/07/15 by Bang‐Yen Chen, Chen, Bang-Yen
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1307.3969

openalex publication_date 2013/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Since J. L. Lagrange initiated in 1760 the study of minimal surfaces of Euclidean 3-space, minimal surfaces in real space forms have been studied extensively by many mathematicians during the last two and half centuries. In contrast, so far very few results on minimal Lorentz surfaces in indefinite space forms are known. Hence, in this paper we investigate minimal Lorentz surfaces in arbitrary indefinite space forms. As a consequence, we obtain several classification results for minimal Lorentz surfaces in indefinite space forms. In particular, we completely classify all minimal Lorentz surfaces in a pseudo-Euclidean space \mathbb E^m_s with arbitrary dimension m and arbitrary index s.

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