# Classification of \(\big (\widetilde{\mathrm {Sp}}(n,\mathbb {R})\times \widetilde{\mathrm {Sp}}(1,\mathbb {R})\big )\)-manifolds

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## Abstract

Let *M* be an analytic complete finite volume pseudo-Riemannian manifold. We characterize the structure of the manifold *M* assuming that the Lie group \(\widetilde{\mathrm {Sp}}(n,\mathbb {R})\times \widetilde{\mathrm {Sp}}(1,\mathbb {R})\) acts isometrically with a dense orbit on *M*, where the \(\widetilde{\mathrm {Sp}}(1,\mathbb {R})\)-orbits are non-degenerated and its dimension satisfies \(\dim (M)\le (n+1)(2n+3)\).

## Keywords

Semisimple Lie groups Rigidity results Pseudo-Riemannian manifolds Isometric actions## Mathematics Subject Classification

57S20 53C24 53C50## References

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