On low-dimensional manifolds with isometric SO 0(p, q)-actions

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Let G be a non-compact simple Lie group with Lie algebra g. Denote with m(g) the dimension of the smallest non-trivial g-module with an invariant non-degenerate symmetric bilinear form. For an irreducible finite volume pseudo-Riemannian analytic manifold M it is observed that dim(M) ≥ dim(G) + m(g) when M admits an isometric G-action with a dense orbit. The Main Theorem considers the case G = SÕ 0(p,q), providing an explicit description of M when the bound is achieved. In such a case, M is (up to a finite covering) the quotient by a lattice of either SÕ 0(p+1, 1,q) or SÕ 0(p,q + 1). © 2012 Springer Science+Business Media, LLC.

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Transformation Groups

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