Abstract
In n+1 dimensional new general relativity including a cosmological constant based on the Weitzenboeck spacetime with absolute parallelism, exact solutions of the gravitational field equations in vacuum for diagonal and space-independent parallel vector fields are found. In usual 3+1 dimensional spacetime, these solutions reduce, for example, to the de Sitter and the Kasner solutions in the limiting case epsilon ..-->.. 0. The parameter epsilon causes a difference to our solutions from those of general relativity. Especially, for the Kasner solution in new general relativity with the condition epsilon < 0, there is a solution which gives a model of the universe expanding in all directions. In general relativity, there is no solution of this type.
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