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Complete Parallel Mean Curvature Surfaces in Two-Dimensional Complex Space-Forms

  • Katsuei Kenmotsu
Article
  • 46 Downloads

Abstract

The purpose of this article is to determine explicitly the complete surfaces with parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. The main results are as follows: when the curvature of the ambient space is positive, there exists a unique such surface up to rigid motions of the target space. On the other hand, when the curvature of the ambient space is negative, there are ‘non-trivial’ complete parallel mean curvature surfaces generated by Jacobi elliptic functions and they exhaust such surfaces.

Keywords

Mean curvature vector Parallel mean curvature surface Jacobi elliptic function Complex space-form 

Mathematics Subject Classification

Primary 53C42 Secondary 53C55 

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Copyright information

© Sociedade Brasileira de Matemática 2018

Authors and Affiliations

  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan

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