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

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

2010-10-01

arxiv.org/abs/1010.0260v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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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