The Euclidean factor of a Hadamard manifold

Abstract

The ideal boundary X ( ∞ ) X(\infty ) of a Hadamard manifold X X is the set of asymptotic classes of rays on X X . We shall characterize the Euclidean factor of X X by information on X ( ∞ ) X(\infty ) . Under the assumption that the diameter of X ( ∞ ) X(\infty ) is π \pi , we call a boundary point that has a unique point of Tits distance π \pi a polar point. We shall show that such points form a standard sphere and compose the boundary of the Euclidean factor of the given Hadamard manifold.