2013/06/25 by Benôıt Daniel, Daniel, Benoit · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1306.5952
openalex publication_date 2013/06/25 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
For a given simply connected Riemannian surface Sigma, we relate the problem of finding minimal isometric immersions of Sigma into S2 x R or H2 x R to a system of two partial differential equations on Sigma. We prove that a constant intrinsic curvature minimal surface in S2 x R or H2 x R is either totally geodesic or part of an associate surface of a certain limit of catenoids in H2 x R. We also prove that if a non constant curvature Riemannian surface admits a continuous one-parameter family of minimal isometric immersions into S2 x R or H2 x R, then all these immersions are associate.