What the fuck is the covariant derivative supposed to represent?
I understand that directional derivatives don't cut it as a good enough operation on tensors because there is no basis for all the tangent spaces and that the covariant derivative is supposed to solve this problem by "connecting" different tangent spaces.
This seems pretty vauge tho, and the way my book presents it is just as a linear map (bilinear technically) that maps tangent vectors to tangent vectors.
I understand that directional derivatives don't cut it as a good enough operation on tensors because there is no basis for all the tangent spaces and that the covariant derivative is supposed to solve this problem by "connecting" different tangent spaces.
This seems pretty vauge tho, and the way my book presents it is just as a linear map (bilinear technically) that maps tangent vectors to tangent vectors.