TITLE: Exponential map on the n-sphere
QUESTION [6 upvotes]: I would like to calculate the exponential map in the n-sphere, however, i don't know how to get started. Someone could give me a tip or bibliographic reference?

REPLY [2 votes]: A good book with examples on the n-sphere is Absil: Optimization Algorithms on Matrix Manifolds. Geodesics at chapter 5 I believe.
An easy way to get geodesics on the n-sphere is to use the embedding map in R^n+1. The connection on the n-sphere is the projection of the connection in R^n+1 (that is flat!). Using this (and the characterization of the tangent vectors to S^n) you can derive the formula that Andrew says.