8) Geodesics

Question 1

Define a geodesic

Answer 1

Question 2

Why are geodesics on a surface independent of choice of parameterization

Answer 2

Question 3

Define a geodesic in terms of geodesic curvature

Answer 3

Question 4

Prove

Answer 4

Question 5

Prove that any (part of) a straight line on a surface is a geodesic

Answer 5

Question 6

Prove that any normal section of a surface is a geodesic

Answer 6

8.1.2. A unit speeed curve γ on a surface σ is a geodesic iff the geodesic curvature of γ is 0 everywhere

Question 7

Geodesic equations

Answer 7

Question 8

Prove geodesic equations

Answer 8

Question 9

Prove that an isometry of 2 surfaces takes the geodesic of one surface to the other

Answer 9

Question 10

Prove

Answer 10

Question 11

There is a unique geodesic

Answer 11

Through any given point of a surface in any given direction

Question 12

Geodesic equations for surface of revolutions

Answer 12

Question 13

Every meridian is?
Every parallel is?

Answer 13

Where 7 and 8 are geodesic equations of surface of revolution

Question 14

Answer 14

Where γ is the shortest path from p to q on a surface and γ_τ is the family of smooth curves from p to q

Question 15

Relate geodesic curve to length of curve

Answer 15