Surfaces with Parallel Normalized Mean Curvature Vector Field in\n Euclidean or Minkowski 4-Space

2018/10/01 by Georgi Ganchev, Ganchev, Georgi, Velichka Milousheva +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #53A07 #53A55 #53B20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1810.01284

openalex publication_date 2018/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study surfaces with parallel normalized mean curvature vector field in\nEuclidean or Minkowski 4-space. On any such surface we introduce special\nisothermal parameters (canonical parameters) and describe these surfaces in\nterms of three invariant functions.\n We prove that any surface with parallel normalized mean curvature vector\nfield parametrized by canonical parameters is determined uniquely up to a\nmotion in Euclidean (or Minkowski) space by the three invariant functions\nsatisfying a system of three partial differential equations. We find examples\nof surfaces with parallel normalized mean curvature vector field and solutions\nto the corresponding systems of PDEs in Euclidean or Minkowski space in the\nclass of the meridian surfaces.\n

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