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On the topology and the geometry of SO(3)-manifolds
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🧮 math.DG
math-phmath.ATmath.MP
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dimensionalgeometrymanifoldstopologybundlecalledcarryingconsider
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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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