The parameters describing the parallel transport of a vector on a manifold, Christoffel symbols, are obtained by taking derivatives of this quantity.
The parameters describing the parallel transport of a vector on a manifold, Christoffel symbols, are obtained by taking derivatives of this quantity. In the Einstein field equations, this quantity multiplies both the scalar curvature and the cosmological constants on the left-hand side. In special relativity, this quantity is represented by a 4-by-4 matrix with no off-diagonal elements whose first diagonal value has opposite sign from the other three, since it represents a time-like quantity; in that case, this quantity is named for Minkowski. In Euclidean space, this quantity is equivalent to the Kronecker delta, which means that distances can be calculated through the generalized Pythagorean theorem. For 10 points, identify this quantity which, for a given space, provides a way to calculate the distance between two points.
The parameters describing the parallel transport of a vector on a manifold, Christoffel symbols, are obtained by taking derivatives of this quantity.
metric tensor [accept Christoffel symbols until the first syllable of "Christoffel" is about to be read]