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arXiv · 1203.0637

Extension of de Rham decomposition theorem via non-Euclidean development

Yacine Chitour·Mauricio Godoy Molina·Petri Kokkonen
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Abstract

In the present paper, we give a necessary and sufficient condition for a Riemannian manifold $(M,g)$ to have a reducible action of a hyperbolic analogue of the holonomy group. This condition amounts to a decomposition of $(M,g)$ as a warped product of a special form, in analogy to the classical de Rham decomposition theorem for Riemannian manifolds. As a consequence of these results and Berger's classification of holonomy groups, we obtain a simple necessary and sufficient condition for the complete controllability of the system of $(M,g)$ rolling against the hyperbolic space.

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Yacine Chitour, Mauricio Godoy Molina, Petri Kokkonen. 2012-03-03. Extension of de Rham decomposition theorem via non-Euclidean development. https://arxiv.org/abs/1203.0637

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