Generalised Surfaces in ${\Bbb{R}}^3$

Brendan Guilfoyle; Wilhelm Klingenberg

Generalised Surfaces in ${\Bbb{R}}^3$

Differential Geometry 2008-11-19 v1

Authors: Brendan Guilfoyle , Wilhelm Klingenberg

Abstract

The correspondence between 2-parameter families of oriented lines in ${\Bbb{R}}^3$ and surfaces in $T{\Bbb{P}}^1$ is studied, and the geometric properties of the lines are related to the complex geometry of the surface. Congruences generated by global sections of $T{\Bbb{P}}^1$ are investigated and a number of theorems are proven that generalise results for closed convex surfaces in ${\Bbb{R}}^3$ .

Keywords

algebraic surfaces curves surfaces with constant mean curvature

Cite

@article{arxiv.math/0406185,
  title  = {Generalised Surfaces in ${\Bbb{R}}^3$},
  author = {Brendan Guilfoyle and Wilhelm Klingenberg},
  journal= {arXiv preprint arXiv:math/0406185},
  year   = {2008}
}

Comments

10 pages, AMS-TEX

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