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

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

2004-06-09

arxiv.org/abs/math/0406185v1

Math. Proc. R. Ir. Acad. 104A(2) (2004) 199-209.

Mathematics

Differential Geometry

10 pages, AMS-TEX

Scientific paper

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 ${\Bbb{R}}^3$.

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