On low-dimensional manifolds with isometric SO 0(p, q)-actions
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.
Publication Source (Journal or Book title)
Ólafsson, G., & Quiroga-Barranco, R. (2012). On low-dimensional manifolds with isometric SO 0(p, q)-actions. Transformation Groups, 17 (3), 835-860. https://doi.org/10.1007/s00031-012-9194-5