# Problem Sheet M

- Problem 1 is shows differentiable homogeneous maps between vector spaces are automatically linear.
- Problem 2 is about building a parallel frame along a curve.
- Problems 3 and 4 explores how to create new connections from old (we will cover this more systematically later).
- Problem 5 is more on our favourite connection on $TS^m$ from the previous problem sheet.
- Problem 6 is about reducing a connection.
- Problem 7 shows how connections behave like tensor derivations.
- Problem 8 gives another way of thinking about flat connections.
*Remark:*If you are not familiar with the universal cover, just skip this question. - Problem 9 discusses left-invariant connections on Lie groups.

Comments and questions?