Gravitation and Two-Dimensional Curved Surfaces

A general method is shown for embedding Riemannian spaces in Euclidean or Minkowskian spaces. This method differs from those of others in that emphasis is placed on the pedagogical value of regarding Minkowskian spaces as Euclidean. The technique is applied to two-dimensional Riemannian surfaces. When the metric of the Riemannian surface depends on only one of the coordinates, the intrinsic geometry of the surface is the same as that of a surface of revolution curved in a Euclidean or Minkowskian three-space. The Schwarzschild radius-time plane and the radius-azimuth plane are given as illustrations of the technique.