2016/12/16 by Georgi Ganchev, Ganchev, Georgi, Krasimir Kanchev +1
Mathematics · Physics and Astronomy · #53A07 #53A10 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #J.2.8
paper · pdf · doi:10.48550/arxiv.1612.05504
openalex publication_date 2016/12/16 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
A space-like surface in Minkowski space-time is minimal if its mean curvature\nvector field is zero. Any minimal space-like surface of general type admits\nspecial isothermal parameters - canonical parameters. For any minimal surface\nof general type parameterized by canonical parameters we obtain Weierstrass\nrepresentations - canonical Weierstrass representations via two holomorphic\nfunctions. We find the expressions of the Gauss curvature and the normal\ncurvature of the surface with respect to this pair of holomorphic functions. We\nfind the relation between two pairs of holomorphic functions generating one and\nthe same minimal space-like surface of general type. The canonical Weierstrass\nformulas allow us to establish geometric correspondence between minimal\nspace-like surfaces of general type and classes of pairs of holomorphic\nfunctions in the Gauss plane.\n