![]() also do not require the concept of a metric. In differential geometry, an affine connection can be defined without reference to a metric, and many additional concepts follow: parallel transport, covariant derivatives, geodesics, etc. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that surface. In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. 10 Applications in classical (non-relativistic) mechanics.8.1 Contravariant derivatives of tensors.6 Relationship to parallel transport and derivation of Christoffel symbols in Riemannian space.5 Transformation law under change of variable.4.4 Ricci rotation coefficients (asymmetric definition).4.3 Connection coefficients in a nonholonomic basis.4.2 Christoffel symbols of the second kind (symmetric definition). ![]() 4.1 Christoffel symbols of the first kind.
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