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Umbilic points

  • #1
who can help me with this:

on an ellipsoid most points are not umbilic, but there are some special places that are. Discuss how to find these points and their connection to lines of curvature.
 

Answers and Replies

  • #2
HallsofIvy
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What is the definition of "umbilic point"?
 
  • #3
an umbilic point is where the directional curvature is the same in all directions. for example, all points on a sphere are umbilic. I know the ellipsoid has four umbilic points but I need help in finding them.
 
  • #4
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This umbilic concept is new to me, but based on your description, I would think that an ellipsoid could have as many as six such points: at the ends of each of the three axes, in the case where all three "radii" are unequal.
 
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