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

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