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Math Forum » Discussions » Inactive » mathqa

Topic: embedding the hyperbolic plane?
Replies: 2   Last Post: Jul 16, 1999 10:14 PM

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Nick Halloway

Posts: 505
Registered: 12/4/04
embedding the hyperbolic plane?
Posted: Jul 11, 1999 12:05 AM
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Can the hyperbolic plane be embedded isometrically in 4-space?

There's an Escher model for the hyperbolic plane that the inside of
a disk.

I figured that maybe in one dimension that could be projected onto a
hyperbola, by

y --> y^2/(1-y^2), y/(1-y^2)

which projects (-1,1) to a hyperbola.

But when I tried to extend this to a projection of a disk into 4-space in
a natural way, it doesn't give an isometric embedding.







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