8: Smooth Maps Between Surfaces

Question 1

smoothness of f does not depend on the choice of local ___

Answer 1

parametrisation

Question 2

a ___ of the surface is a smooth map which assigns to every point p a unit normal vector N(p)

Answer 2

gauss map

Question 3

a gauss map of a regular surface ca always be defined in a ___ of any p

Answer 3

neighbourhood

Question 4

a surface is called ___ is there exists a ___ Gauss map

Answer 4

orientable/global

Question 5

local isometries preserve:
-___ and ___ of vectors
-___ between vectors and curves
-___ of curves

Answer 5

norms/inner products/angles/lengths

Question 6

Global isometries preserve:
-local isometries
-___
-___

Answer 6

distances/areas