A study of the most general form of Bianchi type I space-times is given by using the direct integration and algebraic techniques. In this study we deal with the cases where all the eigenvalues of the Riemann tensor are different. From the above study we have shown that, when the Bianchi type I space-times admit proper projective symmetry, it turns out to be a special class of flat Friedmann Robertson-Walker model.
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