Abstract
Normal coordinate systems for pseudo-Riemannian metrics are investigated from a viewpoint of the theory of partial differential equations. Given a cartesian coordinate system x, a local metric for which x is a normal coordinate system is determined by a metric tensor at the origin and any one of certain three matrix functions. These are related one another by three partial differential equations. Solvability of these equations in C^∞ framework and power series expansion of solutions are discussed.
