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Transitive riemannian isometry groups with nilpotent radicals

C. Gordon (1981)

Annales de l'institut Fourier

Given that a connected Lie group G with nilpotent radical acts transitively by isometries on a connected Riemannian manifold M , the structure of the full connected isometry group A of M and the imbedding of G in A are described. In particular, if G equals its derived subgroup and its Levi factors are of noncompact type, then G is normal in A . In the special case of a simply transitive action of G on M , a transitive normal subgroup G ' of A is constructed with dim G ' = dim G and a sufficient condition is given...

Truncated Lie groups and almost Klein models

Georges Giraud, Michel Boyom (2004)

Open Mathematics

We consider a real analytic dynamical system G×M→M with nonempty fixed point subset M G. Using symmetries of G×M→M, we give some conditions which imply the existence of transitive Lie transformation group with G as isotropy subgroup.

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