Carnot group
In mathematics, a Carnot group is a simply connected nilpotent Lie group, together with a derivation of its Lie algebra such that the subspace with eigenvalue 1 generates the Lie algebra. The subbundle of the tangent bundle associated to this eigenspace is called horizontal. On a Carnot group, any norm on the horizontal subbundle gives rise to a Carnot–Carathéodory metric. Carnot–Carathéodory metrics have metric dilations; they are asymptotic cones (see Ultralimit) of finitely-generated nilpotent groups, and of nilpotent Lie groups, as well as tangent cones of sub-Riemannian manifolds.
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Carnot group
In mathematics, a Carnot group is a simply connected nilpotent Lie group, together with a derivation of its Lie algebra such that the subspace with eigenvalue 1 generates the Lie algebra. The subbundle of the tangent bundle associated to this eigenspace is called horizontal. On a Carnot group, any norm on the horizontal subbundle gives rise to a Carnot–Carathéodory metric. Carnot–Carathéodory metrics have metric dilations; they are asymptotic cones (see Ultralimit) of finitely-generated nilpotent groups, and of nilpotent Lie groups, as well as tangent cones of sub-Riemannian manifolds.
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In mathematics, a Carnot group ...... s of sub-Riemannian manifolds.
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Inom matematiken är en Carnotg ...... erades av Pansu och Mitchell .
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Un groupe de Carnot est un gro ...... l est le groupe de Heisenberg.
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Pierre Pansu
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Pierre
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Pansu
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In mathematics, a Carnot group ...... s of sub-Riemannian manifolds.
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Inom matematiken är en Carnotg ...... erades av Pansu och Mitchell .
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Un groupe de Carnot est un gro ...... l est le groupe de Heisenberg.
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Carnot group
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Carnotgrupp
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Groupe de Carnot
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