Register to reply

Differential geometry

by dori1123
Tags: differential, geometry
Share this thread:
dori1123
#1
Dec14-08, 03:43 PM
P: 11
Given [tex]\{(u,v)\inR^2:u^2+v^2<1\}[/tex] with metric [tex]E = G =\frac{4}{(1-u^2-v^2)^2}[/tex] and [tex]F = 0[/tex]. How can I show that a Euclidean circle centered at the origin is a hyperbolic circle?
Phys.Org News Partner Science news on Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
Doodle Bob
#2
Dec15-08, 04:32 AM
P: 255
Note: rotations about the origin preserve this metric.
dori1123
#3
Dec16-08, 11:28 PM
P: 11
Given [tex]\{(u,v)\inR^2:u^2+v^2<1\}[/tex] with metric [tex]E = G =\frac{4}{(1-u^2-v^2)^2}[/tex] and [tex]F = 0[/tex].
With a Euclidean circle centered at the origin with radius r, how can I find the hyperbolic radius by integrating [tex]\sqrt(E(u')^2+2Fu'v'+G(v')^2)[/tex], what parametrized curve should I use?


Register to reply

Related Discussions
Geometry, Differential Equations, or Differential Geometry Academic Guidance 9
Differential Geometry Calculus & Beyond Homework 7
Should i take differential geometry? Special & General Relativity 4
Differential geometry... Academic Guidance 5
Differential Geometry And Difference Geometry? Differential Geometry 1