Notes on the Deviation of Geodesies and the Fundamental Sealar in a Riemannian Space

Abstract

The principal object if this paper is to study on the deviation of geodesies in a Riemannian space, especially in a Riemannian space of constant curvature, using the properties of the fundamental scalar. Mr. J. L Synge has studied on the deviation of geodesics in such a space, and obtained some res- ults coneerning this subject. But When we utilise the fundanental scalar in.a Riemannian space introdluced by Mr. II. S. Ruse, we can state more precisely the results obtained by Mr. J. L. Synge