The two dimensional torus is one of the most interesting surfaces to study. We parameterize this space and derive the metric tensor. Once we have the metric tensor, the Christoffel symbols are easy to compute by a neat simplifying trick (https://youtu.be/hXTmDtQWvgw). We then write down the geodesic equations. While we can't solve the geodesic equations in all cases, we write down the differential equation of order one to simplify the problem.
#mikethemathematician, #mikedabkowski, #profdabkowski, #tensoranalysis, #geodesics
