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 decomposed it into (i) reguli lying on a family of coaxial hyperboloids of revolution, (ii) the common axis of these hyperboloids, and (iii) the line at infinity of the plane that is perpendicular to the axis of revolution.
The image depicts some of these hyperboloids and the reguli on them.

Created by Mathias Neuwirth (2010) using POV-Ray - The Persistance of Vision Raytracer.

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Last modified on February 18th, 2016.