On some higher-dimensional spacetimes

In 1985, I and Ishihara considered an extension of de Sitter and Nariai's solutions of Rμν = Λgμν in a higher dimensional spacetime. This is a sequel to the above paper in the case where the 6-dimensional space-time consists of 4-dimensional isotropic homogeneous space and two-dimensional space with Kantowski-Sach's form. It is shown that the vacuum equations admit such a solution that the 4-dimensional space is 3 famous forms of the de Sitter space-time and the 2-dimensional one is Nariai's static form. (author)