CMC-1 Surfaces in Hyperbolic 3-space using the Bianchi-Calo method

Levi Lopes de Lima; Pedro Roitman

CMC-1 Surfaces in Hyperbolic 3-space using the Bianchi-Calo method

微分几何 2007-05-23 v1 历史与综述

作者: Levi Lopes de Lima , Pedro Roitman

摘要

In this note we present a method for constructing CMC-1 surfaces in hyperbolic 3-space $\bfH^3(-1)$ in terms of holomorphic data first introduced in Bianchi's Lezioni di Geometria Differenziale of 1927, therefore predating by many years the modern approaches due to Bryant, Small and others. Besides its obvious historical interest, this note aims to complement Bianchi's analysis by deriving explicit formulae for CMC-1 surfaces and comparing the various approaches encountered in the literature.

引用

@article{arxiv.math/0110021,
  title  = {CMC-1 Surfaces in Hyperbolic 3-space using the Bianchi-Calo method},
  author = {Levi Lopes de Lima and Pedro Roitman},
  journal= {arXiv preprint arXiv:math/0110021},
  year   = {2007}
}

备注

13 pages, 4 figures

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