A Note on the Positive Constant Curvature Space

We construct a positive constant curvature space by identifying some points along a Killing vector in a de Sitter Space. This space is the counterpart of the three-dimensional Schwarzschild-de Sitter solution in higher dimensions. This space has a cosmological event horizon, and is of the topology ${\cal M}_{D-1}\times S^1$, where ${\cal M}_{D-1}$ denotes a $(D-1)$-dimensional conformal Minkowski spacetime.