🎬the geometrical meaning of the Christoffel symbols in flat Euclidean space using the non-Cartesian s

Christoffel symbols are necessary to describe parallel transport in curvilinear coordinate systems, even in flat space. While a vector being parallel transported maintains a constant direction in Cartesian coordinates, its components in a rotating basis like spherical coordinates are constantly changing. The non-zero Christoffel symbols precisely quantify this rate of change, ensuring that the covariant derivative—which accounts for the change in both the vector's components and the basis vectors themselves—is zero, correctly representing a constant vector.

Calculation of the Metric Tensor and Christoffel Symbols in Spherical Coordinates | Proof and Derivationviadean on Notion