Rough Notes Written on a Moving Train

A Second Look at Tensors, Covariant Differentiation and Curvature

by bob jantzen  [March 1990]

University of Rome "La Sapienza", Dipartimento di Fisica, Corso di Fisica Teorico (Ruffini)

A vector space and its dual, with basis and dual basis and modern tensor notation are introduced and then tied to the tangent space of ordinary space in Cartesian coordinates, then transformed to spherical coordinates. In this context parallel transport and covariant differentiation are introduced, leading to the vanishing curvature tensor of flat space.