1. CMB 2002 (vol 45 pp. 378)
|The Local MÃ¶bius Equation and Decomposition Theorems in Riemannian Geometry |
A partial differential equation, the local M\"obius 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 M\"obius equation and an additional partial differential equation.
Keywords:submersion, MÃ¶bius equation, twisted product, warped product, product Riemannian manifolds