On the product of affine manifolds and the generalized de Rham splitting theorem

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1993 English Publisher:Springer Science and Business Media LLCJournal:Periodica Mathematica Hungarica, volume 26, pages 15-30 (issn: 0031-5303, eissn: 1588-2829,

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Authors: Major, E. I.;

doi: 10.1007/bf01875878

On the product of affine manifolds and the generalized de Rham splitting theorem

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Abstract

A de Rham decomposition theorem for arbitrary affine connections, satisfying a certain curvature condition, is proved. This generalizes the theorems of de Rham or \textit{S. Kobayashi} and \textit{K. Nomizu} [Foundations of differential geometry, Vols. I and II, Interscience (New York 1963; Zbl 0119.375 and 1969; Zbl 0175.485)]. The very elaborate proof follows closely that from the book cited above.

Related Organizations

The Ohio State University
United States
Hungarian Academy of Sciences
Hungary

Keywords

affine connections, Linear and affine connections, de Rham decomposition theorem

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