On low-dimensional manifolds with isometric SO0(p, q)-actions

Let G be a non-compact simple Lie group with Lie algebra . Denote with m() the dimension of the smallest non-trivial -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) a parts per thousand yenaEuro parts per thousand dim(G) + m() when M admits an isometric G-action with a dense orbit. The Main Theorem considers the case , 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 (SO) over tilde (0) (p + 1; q) or (SO) over tilde (0) (p; q + 1).