Neeb, Karl-Hermann Ordered symmetric spaces. (English) Zbl 0795.53049 Bureš, J. (ed.) et al., The proceedings of the 11th winter school on geometry and physics held in Srní, Czechoslovakia, January 5-12, 1991. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 30, 21-26 (1993). A conal manifold \(M\) is a smooth manifold endowed with a field of closed convex cones \(\theta (x)\) in the tangent spaces \(T_ xM\). Homogeneous and symmetric conal manifolds are defined in a natural way, and the “conal order” on \(M\) can be also defined. \(M\) is then said to be globally orderable if the conal order makes \(M\) a partially ordered set. \(M\) is said to be globally hyperbolic if every closed order interval is a compact subset of \(M\). The last definition is important in many applications (such as relativity and harmonic analysis on symmetric spaces) and some necessary and sufficient conditions for this property are given without proof.For the entire collection see [Zbl 0777.00026]. Reviewer: O.Kowalski (Praha) MSC: 53C35 Differential geometry of symmetric spaces 53C30 Differential geometry of homogeneous manifolds 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics Keywords:conal order; conal manifold; symmetric conal manifolds; globally hyperbolic × Cite Format Result Cite Review PDF