2022•Unpublished venueRequires access
Tensor calculus
Ray d’Inverno, James Vickers
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Abstract
Abstract Chapter 6 introduces tensor calculus and deals with two important generalizations of partial derivatives, namely the Lie derivative and the covariant derivative. The metric tensor, which is used to measure distance on a manifold, is introduced and it is shown how this defines the metric connection which is used to define the covariant derivative. The very important notion of Riemann curvature is introduced using covariant derivatives and an explicit expression is derived for the Riemannian tensor. It is also shown how to decompose the curvature into a Ricci tensor part and a Weyl part