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#1 2014-03-22 04:33:58
- ShivamS
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- Registered: 2011-02-07
- Posts: 3,648
Differential Geometry
Check that if there are no umbilic points and the parameter curves are lines of curvature, then F = m = 0 and we have the principal curvatures k1 = L/E and k2 = n/G. Conversely, prove that if F = m = 0, then the parameter curves are lines of curvature.
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#2 2014-03-23 07:13:02
- eigenguy
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- Registered: 2014-03-18
- Posts: 78
Re: Differential Geometry
That would require knowing what F, m, L, E, n, G all are defined to be.
"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich
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