On the topology and the geometry of SO(3)-manifolds
Differential Geometry
2013-11-05 v1 Mathematical Physics
Algebraic Topology
math.MP
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.
Keywords
Cite
@article{arxiv.1010.0260,
title = {On the topology and the geometry of SO(3)-manifolds},
author = {Ilka Agricola and Julia Becker-Bender and Thomas Friedrich},
journal= {arXiv preprint arXiv:1010.0260},
year = {2013}
}
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15 pages