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Within the scope of anisotropic non-diagonal Bianchi type-II, VIII and IXspacetime it is shown that the off-diagonal components of the correspondingmetric impose severe restrictions on the components of the energy momentumtensor in general. If the energy momentum tensor is considered to be diagonalone, the spacetime, expect a partial case of BII, becomes locally rotationallysymmetric.

Some remarks on Bianchi type-II, VIII and IX models