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Mathematical Preliminaries

For exterior position vectors, I am using capital letters (e.g. R\boldsymbol{R}). For general vectors, I am using lowercase letters (e.g. v\boldsymbol{v}).

Tensor Calculus IntroductionCovariance and ContravarianceArc Length and Metric TensorGradientGeodesics and Christoffel SymbolsCovariant DerivativeLie Bracket and Torsion TensorRiemann TensorRicci TensorLie DerivativeKilling Vectors