Abstract
This chapter examines relations between covariant derivatives and metrics. It covers metric compatible covariant derivatives; torsion free covariant derivatives on T*M; the Levi-Civita connection/covariant derivative; a formula for the Levi-Civita connection; covariantly constant sections; an example of the Levi-Civita connection; and the curvature of the Levi-Civita connection.
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