Differential Geometry and Geometric Structures
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Students' Work: Elliptic Linear Congruence


An elliptic linear congruence is a particular set of lines which sends precisely one line through each point of the three-dimensional real projective space. It is also called a regular spread. Our example admits - from a Euclidean point of view - a rotational symmetry.
This set of lines can be split into reguli lying on a family of hyperbolic paraboloids which share two generators, one of them being at infinity.
The image depicts some of these paraboloids and the reguli on them.

Created by Katharina Schneider (2010) using POV-Ray - The Persistance of Vision Raytracer.

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Elliptic Linear Congruence
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Last modified on February 18th, 2016.