|
|
|
|
| (1) | Read chapter 3 of Do Carmo: “Geodesics and convex neighborhoods”. |
| (2) | Let  and  be connected Riemannian manifolds. Let  be two isometries from to . Suppose that for one point  ,  and  . Prove that  . |
| (3) | Suppose that a metric on  in local coordinates  has the form  . This means that  ,  , and  . Show that all curves  =constant are geodesics. |
| (4) | Do Carmo, chapter 3, problem 1 (surfaces of revolution). |
| (5) | Do Carmo, chapter 3, problems 5 and 6 (Killing fields). |
|
| Created by MicroPress TeXpider. |