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# The Local Möbius Equation and Decomposition Theorems in Riemannian Geometry

Published:2002-09-01
Printed: Sep 2002
• Manuel Fernández-López
• Eduardo García-Río
• Demir N. Kupeli
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## Abstract

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, Möbius equation, twisted product, warped product, product Riemannian manifolds
 MSC Classifications: 53C12 - Foliations (differential geometric aspects) [See also 57R30, 57R32] 58J99 - None of the above, but in this section