Vectors and tensors in curved space
Kristopher A. Innanen
Elsewhere in this report we develop the idea of navigating in model space (e.g., to construct the best estimate of an Earth model) not as usual, by being guided by an external objective function and its derivatives, but rather, by following the simplest possible paths in a space that is curved by the objective function. This requires ideas of Riemannian curvature, parallel displacement, and geodesics to be reviewed. This review can be considered as an addendum to the review on tensor analysis in non-Cartesian coordinate systems in the 2020 report.