Some Higher Demensional Vacuum Solutions of Einstein Equations with a Cosmological Constant

Abstract
As the first step to obtain a higher dimensional model of the universe, some solutions of vacuum Einstein equations with a non-vanishing cosmological term, whose topology is M2(2-dim space-time)⊗Nn(n-dim external space with a constant curvature k=+1, 0, -1), are studied. In the case n=3, some simple solutions are obtained.

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