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In this note we classify a certain family of solutions of Lovelock gravity inthe Chern-Simons (CS) case, in arbitrary (odd) dimension greater than four. Thespacetime is characterized by admitting a metric that is a warped product of atwo-dimensional spacetime M2 and an (a priori) arbitrary Euclidean basemanifold Sigma(d-2) of dimension d-2. We show that the solutions are naturallyclassified in terms of the equations that restrict the base manifold. Accordingto the strength of such constraints we found the following branches in whichSigma(d-2) has to fulfill: a Lovelock equation with a single vacuum (EuclideanLovelock Chern-Simons in dimension d-2), a single scalar equation that is thetrace of an Euclidean Lovelock CS equation in dimension d-2, or finally adegenerate case in which the base manifold is not restricted at all. We showthat all the cases have some degeneracy in the sense that the metric functionsare not completely fixed by the field equations. This result extends the staticfive-dimensional case previously discussed in Phys.Rev. D76 (2007) 064038, andit shows that in the CS case, the inclusion of higher powers in the curvaturedoes not introduce new branches of solutions in Lovelock gravity. Finally wecomment on how the inclusion of a non-vanishing torsion and matter fields maymodify this analysis.

All the solutions of the form M2(warped)x\Sigma(d-2) for Lovelock gravity in vacuum in the Chern-Simons case