Lines of curvature of circular parabola
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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
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add a comment |
$begingroup$
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
$endgroup$
$begingroup$
Use the symmetry?
$endgroup$
– random
Dec 4 '18 at 0:43
add a comment |
$begingroup$
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
$endgroup$
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
$begingroup$
Use the symmetry?
$endgroup$
– random
Dec 4 '18 at 0:43
add a comment |
$begingroup$
Use the symmetry?
$endgroup$
– random
Dec 4 '18 at 0:43
$begingroup$
Use the symmetry?
$endgroup$
– random
Dec 4 '18 at 0:43
$begingroup$
Use the symmetry?
$endgroup$
– random
Dec 4 '18 at 0:43
add a comment |
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$begingroup$
Use the symmetry?
$endgroup$
– random
Dec 4 '18 at 0:43