Finding Umbilic Points on an Ellipsoid & Their Connection to Lines of Curvature

[halvizo1031]

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.

 

[HallsofIvy]

What is the definition of "umbilic point"?

 

[halvizo1031]

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.

 

[Mark44]

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.