An Elementary Proof of the Existence of Isothermal Parameters on a Surface
An Elementary Proof of the Existence of Isothermal Parameters on a Surface
shiing-shen chern 1. Introduction.Let (1) ds2 = E(x, y)dx2 + 2F(x, y)dxdy + G(x, y)dy2, EG -F2 > 0, E > 0, be a positive definite Riemann metric of two dimensions defined in a neighborhood of a surface with the local coordinates x, y.By isothermal parameters we mean local coordinates …