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De Rham decomposition of affinely connected manifolds

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Abstract

This article contains an extension of the de Rham decomposition theorem to affinely connected manifolds which may have torsion. Our proof is based on a geometric homotopy lemma, which allows a simple and comparatively short proof of this result by means of the Cartan-Ambrose-Hicks theorem.

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Authors and Affiliations

  1. Mathematisches Institut der Universität zu Köln, Weyertal 86-90, 5000, Köln 41, Federal Republic of Germany

    Thomas Meumertzheim

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  1. Thomas Meumertzheim
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Meumertzheim, T. De Rham decomposition of affinely connected manifolds. Manuscripta Math 66, 413–429 (1990). https://doi.org/10.1007/BF02568506

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  • DOI: https://doi.org/10.1007/BF02568506

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