This Problem Sheet is based on Lectures 30 and 31

• Problem 1 asks you to prove a more general version of Lemma 31.5.
• Problem 2 is more on our favourite connection on $TS^n$ from Problem Sheet N.
• Problem 3 explores how to define a connection on the dual vector bundle. (We will cover this more systematically later.)
• Problem 4 looks horrendous, but it is mainly an exercise in unravelling the formalism. (The solution is much shorter than the statement of the problem!)