Horospheres and hyperbolic spaces (Q2864702)

Let \(X\) be a Hadamard manifold. The authors apply the stable Jacobi tensor along horospherical foliations of \(X\), to give a characterization of the real space form by means of the second fundamental form of the horospheres. The complex space form, the quaternionic space form and the other rank-one symmetric spaces of non-compact type are also similarly characterized. They also present some geometrical characterization of horospheres.