Abstract
The field equations following from a LagrangianL(1/L)(−g)1/2[(1/2)R+l 2(αR lk R lk +βR 2)] will be considered for Bianchi type-I homogeneous models. Thereby the special case,α+3β=0, is considered qualitatively for axially symmetric anisotropic metrics. Generically, the solutions have both past and future singularities, but it will be proven by topological arguments that the two-dimensional space of solutions possesses a one-parameter subspace of solutions with a behavior similar to the Kasner solution.
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