Lines of curvature of circular parabola
Given the circular parabola $x(θ,ϕ)=(θcos(ϕ),θsin(ϕ),θ^2)$, how would I show that the curvature lines are the parallels (circles) and the meridians (parabolas)?
differential-geometry
asked Dec 4 '18 at 0:23
JimJim
1
add a comment |
Given the circular parabola $x(θ,ϕ)=(θcos(ϕ),θsin(ϕ),θ^2)$, how would I show that the curvature lines are the parallels (circles) and the meridians (parabolas)?
differential-geometry
asked Dec 4 '18 at 0:23
JimJim
1
Use the symmetry?
– random
Dec 4 '18 at 0:43
add a comment |
Given the circular parabola $x(θ,ϕ)=(θcos(ϕ),θsin(ϕ),θ^2)$, how would I show that the curvature lines are the parallels (circles) and the meridians (parabolas)?
differential-geometry
asked Dec 4 '18 at 0:23
JimJim
1
Given the circular parabola $x(θ,ϕ)=(θcos(ϕ),θsin(ϕ),θ^2)$, how would I show that the curvature lines are the parallels (circles) and the meridians (parabolas)?
differential-geometry
differential-geometry
asked Dec 4 '18 at 0:23
JimJim
1
asked Dec 4 '18 at 0:23
JimJim
1
asked Dec 4 '18 at 0:23
JimJim
1
asked Dec 4 '18 at 0:23
JimJim
1
asked Dec 4 '18 at 0:23
JimJim
1
1
Use the symmetry?
– random
Dec 4 '18 at 0:43
add a comment |
Use the symmetry?
– random
Dec 4 '18 at 0:43
Use the symmetry?
– random
Dec 4 '18 at 0:43
Use the symmetry?
– random
Dec 4 '18 at 0:43
add a comment |
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Use the symmetry?
– random
Dec 4 '18 at 0:43