Gauss' Theory of Curved Surface
Einstein, in his theory of general relativity, used Riemannian geometry which is a generalization of Gauss' theory of curved surface. So if you can understand Gauss' theory, it will help your understanding of tensor and metric. The following figure shows essentials of this. Recall that not only the length of a curve, but also the whole geometry of the curved surface is determined if we know the formula for the line element ds; and this in turn is determined by metric.
Last modified March 28, 2003. (c) Soshichi Uchii
