|
In mathematics, specifically in differential geometry, isothermal coordinates on a Riemannian manifold are local coordinates where the metric is conformal to the Euclidean metric. This means that in isothermal coordinates, the Riemannian metric locally has the form : where is a smooth function. Isothermal coordinates on surfaces were first introduced by Gauss. Korn and Lichtenstein proved that isothermal coordinates exist around any point on a two dimensional Riemannian manifold. On higher-dimensional Riemannian manifolds a necessary and sufficient condition for their local existence is the vanishing of the Weyl tensor and of the Cotton tensor. ==Isothermal coordinates on surfaces== proved the existence of isothermal coordinates on an arbitrary surface with a real analytic metric, following results of on surfaces of revolution. Results for Hölder continuous metrics were obtained by and . Later accounts were given by , , and . A particularly simple account using the Hodge star operator is given in . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「isothermal coordinates」の詳細全文を読む スポンサード リンク
|