Causal characters of zero mean curvature surfaces of Riemann type in the Lorentz-Minkowski 3-space

2015/10/26 by Shintaro Akamine, Akamine, Shintaro
Mathematics · Physics and Astronomy · #53A10 #53A35 #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1510.07451

openalex publication_date 2015/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A zero mean curvature surface in the Lorentz-Minkowski 3-space is said to be of Riemann-type if it is foliated by circles and at most countably many straight lines in parallel planes. We classify all zero mean curvature surfaces of Riemann-type according to their causal characters, and as a corollary, we prove that if a zero mean curvature surface of Riemann-type has exactly two causal characters, then the lightlike part of the surface is a part of a straight line.

Citations

• Zero mean curvature entire graphs of mixed type in Lorentz-Minkowski 3-space

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