how the Kronecker delta and Christoffel symbols behave in a Cartesian coordinate system

In Cartesian coordinates, the basis vectors are constant and do not change with position. This is the fundamental reason why tensor calculations are simplified in this system. As you move the probe vector to a new location, the basis vectors that appear with it are identical in both direction and magnitude to the basis vectors at the origin. This visualizes a crucial concept: tensors in Cartesian coordinates don't require Christoffel symbols to account for changing basis vectors, because the basis vectors simply don't change.

$\complement\cdots$Counselor

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