Differential Geometry From Singularity Theory Viewpoint by Izumiya Shyuichi

Author:Izumiya, Shyuichi
Language: eng
Format: epub
ISBN: 9789814590464
Publisher: World Scientific Publishing Company
Published: 2016-07-24T16:00:00+00:00

for i = 1 or 2, that is, the ridge is the set of points where a principal curvature is extremal along its associated lines of principal curvature.

Proof. Consider, for example, the focal set associated to the principal curvature κ1 which is parametrised by

The directions xu1 and xu2 are principal directions at all points in U so Nui = −κixui, i = 1, 2. Differentiating ε1 and dropping the argument, we get

A point p = x(u1, u2) is on the ridge if the focal set is singular at ε1(u1, u2). As p is not an umbilic point, the vectors ∂ε1/∂u1 and ∂ε1/∂u2 are linearly dependent at (u1, u2) if and only if

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.