The Local Mobius Equation and Decomposition Theorems in Riemannian Geometry

Abstract

A partial differential equation, the local Mobius equation, is introduced in Riemannian geometry which completely characterizes the local twisted product structure of a Riemannian manifold. Also the characterizations of warped product and product structures of Riemannian manifolds are made by the local Mobius equation and an additional partial differential equation.