11: Curves on Surfaces

Question 1

if x is a ___ parametrisation of a surface then the coordinate curves are lines of curvature

Answer 1

principal

Question 2

if x is a principal parametrisation and if ___ points of S are isolated then the only lines of curvature are the ___ curves

Answer 2

umbilic/coordinate

Question 3

a curve on a regular surface is called an ___ curve if its normal curvature vanishes

Answer 3

asymptotic

Question 4

Geodesic curvature is an ___ quantity

Answer 4

intrinsic