Geodesic Coordinates/Riemannian Normal Coordinates

Among the many potential changes of coordinates that we can make there is a very useful one in the study of curvature: geodesic or Riemannian normal coordinates. These coordinates are chosen so that the Christoffel symbols vanish at a particular point called the pole. In these coordinates, several terms in the Riemann-Christoffel tensor vanish. This is an effective coordinate system for dealing with covariant differentiation of the Riemann-Christoffel tensor as we will seen when we prove the Bianchi Identity. #mikethemathematician, #mikedabkowski, #profdabkowski, #tensoranalysis