🎬illustrate the relationship between the covariant derivative and the gradient of a scalar field on a

This demo is that for a scalar field, the covariant derivative is equivalent to the gradient vector. The visualization shows this by demonstrating that the gradient vector, which always points "uphill" in the direction of the steepest increase in the scalar field's value, accurately represents the covariant derivative in this context.

The Metric Tensor Covariant Derivatives and Tensor Densities | Condensed Notesviadean on Notion