“Principal orbit type theorem”的意思、由来-开放百科全书

词条

Principal orbit type theorem

释义

Definitions
References

In mathematics, the principal orbit type theorem states that compact Lie group acting smoothly on a connected differentiable manifold has a principal orbit type.

Definitions

Suppose G is a compact Lie group acting smoothly on a connected differentiable manifold M.

An isotropy group is the subgroup of G fixing some point of M.
An isotropy type is a conjugacy class of isotropy groups.
The principal orbit type theorem states that there is a unique isotropy type such that the set of points of M with isotropy groups in this isotropy type is open and dense.
The principal orbit type is the space G/H, where H is a subgroup in the isotropy type above.

References

{{citation|mr=0889050

|last=tom Dieck|first= Tammo
|title=Transformation groups
|series=de Gruyter Studies in Mathematics|volume= 8|publisher= Walter de Gruyter & Co.|place= Berlin|year= 1987|isbn= 3-11-009745-1 |pages=42–43}}

2 : Lie groups|Group actions (mathematics)

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