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arXiv · 1010.0260

On the topology and the geometry of SO(3)-manifolds

Ilka Agricola·Julia Becker-Bender·Thomas Friedrich
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Abstract

Consider the nonstandard embedding of SO(3) into SO(5) given by the 5-dimensional irreducible representation of SO(3), henceforth called SO(3)_\ir. In this note, we study the topology and the differential geometry of 5-dimensional Riemannian manifolds carrying such an SO(3)_\ir structure, i.\,e. with a reduction of the frame bundle to SO(3)_\ir.

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Ilka Agricola, Julia Becker-Bender, Thomas Friedrich. 2010-10-01. On the topology and the geometry of SO(3)-manifolds. https://arxiv.org/abs/1010.0260

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