DescriptionIn this paper, we explore various notations and definitions, in Riemannian Geometry,
which were created during the past century. Next, we developed a few clear examples from
the book RIEMANNIAN GEOMETRY written by Do Carmo and explain the article A THE-
OREM ON THE AFFINE TRANSFORMATION GROUP OF A RIEMANNIAN MANIFOLD
written by S.Kobayashi in detail.