Metric Compatible Covariant Derivatives
Abstract
This paper, sixth in a series of eight, uses the geometric calculus on manifolds developed in previous papers of the series to introduce through the concept of a metric extensor field g a metric structure for a smooth manifold M. The associated Christoffel operators, a notable decomposition of that object and the associated Levi-Civita connection field are given. The paper introduces also the concept of a geometrical structure for a manifold M as a triple (M,g,gamma), where gamma is a connection extensor field defining a parallelism structure for M . Next, the theory of metric compatible covariant derivatives is given and a relationship between the connection extensor fields and covariant derivatives of two deformed (metric compatible) geometrical structures (M,g,gamma) and (M,eta,gamma') is determined.
Keywords
Cite
@article{arxiv.math/0501561,
title = {Metric Compatible Covariant Derivatives},
author = {W. A. Rodrigues and V. V. Fernandez and A. M. Moya},
journal= {arXiv preprint arXiv:math/0501561},
year = {2007}
}