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Unique decomposition of Riemannian manifolds

Author(s): J.-H. Eschenburg; E. Heintze
Journal: Proc. Amer. Math. Soc. 126 (1998), 3075-3078.
MSC (1991): Primary 53C20; Secondary 53C12
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Abstract: We prove an extension of de Rham's decomposition theorem to the non-simply connected case.

References:

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G. de Rham: Sur la réductibilité d'un espace de Riemann, Comm. Math. Helv. 26 (1952), 328 - 344 MR 14:584a

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M. Gromov: Almost flat manifolds, J. Diff. Geom. 13 (1978), 231 - 241 MR 80h:53041

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S. Kobayashi, K. Nomizu: Foundations of Differential Geometry, vol. 1, Interscience, Wiley, New York 1963 MR 27:2945

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R. Maltz: The de Rham product decomposition, J. Diff. Geom. 7 (1972), 161 - 174 MR 48:2930

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R. Pantilie: A simple proof of the de Rham decomposition theorem, Bull. Math. Soc. Sc. Math. Roumanie 36 (84) (1992), 341 - 343 MR 95m:53068

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H. Takagi: Notes on the cancellation of Riemannian manifolds, Tôhoku Math. J. 32 (1980), 411 - 417 MR 82g:53048

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K. Uesu: Cancellation law for Riemannian direct products, J. Math. Soc. Japan 36 (1984), 53 - 62 MR 85c:53072

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Additional Information:

J.-H. Eschenburg
Affiliation: Institut fur Mathematik, Universität Augsburg, D-86135 Augsburg, Germany
Email: eschenburg@math.uni-augsburg.de

E. Heintze
Affiliation: Institut fur Mathematik, Universität Augsburg, D-86135 Augsburg, Germany
Email: heintze@math.uni-augsburg.de

DOI: 10.1090/S0002-9939-98-04630-9
PII: S 0002-9939(98)04630-9
Keywords: Riemannian products, indecomposable Riemannian manifolds, irreducible Riemannian manifolds, de Rham's theorem
Received by editor(s): February 28, 1997
Communicated by: Christopher Croke
Copyright of article: Copyright 1998, American Mathematical Society

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