One Parameter Groups of Deformations in Riemannian Spaces

Abstract

Taking a finite one parameter transformation of a Lie group generated by the infinitesimal transformation D = u^r ∂/∂x^r in a space either Riemannian or of affine connection, Kosambi was the first to suggest the idea that if the group G operates in that space, the geometric objects could be generated by suitable operators associated with the given Lie group.