The distribution of symmetry of a naturally reductive nilpotent Lie group
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🧮 math.DG
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distributionnaturallyreductivesymmetrygroupnilpotentaddresscoincides
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We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides with the invariant distribution induced by the set of fixed vectors of the isotropy. This extends a known result on compact naturally reductive spaces. We also address the study of the quotient by the foliation of symmetry.
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