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The Local Möbius Equation and Decomposition Theorems in Riemannian Geometry

Published online by Cambridge University Press:  20 November 2018

Manuel Fernández-López ,
Eduardo García-Río  and
Demir N. Kupeli
Manuel Fernández-López
Affiliation:
Department of Geometry and Topology Faculty of Mathematics University of Santiago de Compostela 15782 Santiago de Compostela Spain, e-mail: [email protected]
Eduardo García-Río
Affiliation:
Department of Geometry and Topology Faculty of Mathematics University of Santiago de Compostela 15782 Santiago de Compostela Spain, e-mail: [email protected]
Demir N. Kupeli
Affiliation:
Department of Mathematics Atιlιm University İncek 06836 Ankara Turkey email: [email protected]
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Abstract

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A partial differential equation, the local Möbius 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 Möbius equation and an additional partial differential equation.

Keywords

53C1258J99submersionMöbius equationtwisted productwarped productproduct Riemannian manifolds
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 3 , 01 September 2002 , pp. 378 - 387
Copyright
Copyright © Canadian Mathematical Society 2002

References

[1] Kühnel, W. and Rademacher, H.-B., Conformal Vector Fields on Pseudo-Riemannian Spaces. Differential Geom. Appl. 7 (1997), 7–1997.Google Scholar
[2] Osgood, B. and Stowe, D., The Schwarzian Derivative and Conformal Mapping of Riemannian Manifolds. Duke Math. J. 67 (1992), 67–1992.Google Scholar
[3] Ponge, R. and Reckziegel, H., Twisted Products in Pseudo-Riemannian Geometry. Geom. Dedicata 48 (1993), 48–1993.Google Scholar
[4] Vilms, J., Totally Geodesic Maps. J. Differential Geom. 4 (1970), 4–1970.Google Scholar