The Euclidean factor of a Hadamard manifold

Abstract:

The ideal boundary $X(\infty )$ of a Hadamard manifold $X$ is the set of asymptotic classes of rays on $X$. We shall characterize the Euclidean factor of $X$ by information on $X(\infty )$. Under the assumption that the diameter of $X(\infty )$ is $\pi$, we call a boundary point that has a unique point of Tits distance $\pi$ 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.