- #1
- 7,005
- 10,443
Hi: I am going over Lee's Riemm. mflds, and there is an exercise that asks:
Let M<M' (< is subset) be an embedded submanifold.
Show that any vector field X on M can be extended to a vector field on M'.
Now, I don't know if he means that X can be extended to the _whole_ of
M', because otherwise, there is a counterexample:
dt/t on (0,1) as a subset of IR cannot be extended to the whole of IR.
Anyone know?.
What Would Gauss Do?
Let M<M' (< is subset) be an embedded submanifold.
Show that any vector field X on M can be extended to a vector field on M'.
Now, I don't know if he means that X can be extended to the _whole_ of
M', because otherwise, there is a counterexample:
dt/t on (0,1) as a subset of IR cannot be extended to the whole of IR.
Anyone know?.
What Would Gauss Do?