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

We study surfaces with parallel normalized mean curvature vector field in Euclidean or Minkowski 4-space. On any such surface we introduce special isothermal parameters (canonical parameters) and describe these surfaces in terms of three invariant functions. We prove that any surface with parallel n...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2018-10
Main Authors: Ganchev, Georgi, Milousheva, Velichka
Format: Article
Language:English
Subjects:
Curvature
Demand
Euclidean geometry
Fields (mathematics)
Invariants
Mathematical analysis
Minkowski space
Parameters
Partial differential equations
Production planning
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study surfaces with parallel normalized mean curvature vector field in Euclidean or Minkowski 4-space. On any such surface we introduce special isothermal parameters (canonical parameters) and describe these surfaces in terms of three invariant functions. We prove that any surface with parallel normalized mean curvature vector field parametrized by canonical parameters is determined uniquely up to a motion in Euclidean (or Minkowski) space by the three invariant functions satisfying a system of three partial differential equations. We find examples of surfaces with parallel normalized mean curvature vector field and solutions to the corresponding systems of PDEs in Euclidean or Minkowski space in the class of the meridian surfaces.
ISSN:2331-8422