# On the topology and the geometry of SO3-manifolds - Mathematics > Differential Geometry

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Abstract: Consider the nonstandard embedding of SO3 into SO5 given by the5-dimensional irreducible representation of SO3, henceforth called SO3 \ir.In this note, we study the topology and the differential geometry of5-dimensional Riemannian manifolds carrying such an SO3 \ir structure, i.\,e.with a reduction of the frame bundle to SO3 \ir.

Autor: Ilka Agricola, Julia Becker-Bender, Thomas Friedrich

Fuente: https://arxiv.org/