curves on quadrics - sci.math

Message from discussion curves on quadrics

Ken Pledger

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More options May 18, 6:04 pm

Newsgroups: sci.math

From: Ken Pledger <ken.pled...@mcs.vuw.ac.nz>

Date: Mon, 19 May 2008 10:04:41 +1200

Local: Sun, May 18 2008 6:04 pm

Subject: Re: curves on quadrics

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In article
<f4b27853-16cf-45fb-8559-3df2021bf...@d1g2000hsg.googlegroups.com>,
Dmitry Sustretov <dmitry.sustre...@gmail.com> wrote:

> .... By the way, are hyperboloid and hyperbolic paraboloid (that
> have been mentioned) the only quadric surfaces that are ruled?

Your geometry here is presumably affine or Euclidean, not purely
projective.

The hyperboloid of one sheet and the hyperbolic paraboloid are the
only proper (non-degenerate) quadrics with real rulings, yes. Cones,
cylinders and plane-pairs also have real rulings, and if you allow
complex coordinates then even ellipsoids are ruled.

Ken Pledger.

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