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Prescribed Riemannian Symmetries
2021
Symmetry, Integrability and Geometry: Methods and Applications
Given a smooth free action of a compact connected Lie group G on a smooth compact manifold M , we show that the space of G-invariant Riemannian metrics on M whose automorphism group is precisely G is open dense in the space of all G-invariant metrics, provided the dimension of M is "sufficiently large" compared to that of G. As a consequence, it follows that every compact connected Lie group can be realized as the automorphism group of some compact connected Riemannian manifold; this recovers
doi:10.3842/sigma.2021.030
fatcat:654hf4c3yrc3hhsaqvyncgorjq