differential geometry


by dori1123
Tags: differential, geometry
dori1123
dori1123 is offline
#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
Review: With Galaxy S5, Samsung proves less can be more
Making graphene in your kitchen
Study casts doubt on climate benefit of biofuels from corn residue
Doodle Bob
Doodle Bob is offline
#2
Dec15-08, 04:32 AM
P: 255
Note: rotations about the origin preserve this metric.
dori1123
dori1123 is offline
#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