Supersymmetric dS_n solutions for n 5 in D=11 supergravity

We determine the necessary and sufficient conditions for warped product dS(n) solutions, 5 <= n <= 10, to preserve supersymmetry in D = 11 supergravity, without assuming factorization of the Killing spinors. We prove that for 7 <= n <= 1 0, all such solutions are flat, with vanishing four-form. We also show that the only warped product dS(6) solutions are either the maximally supersymmetric AdS(7) x S-4 solution, or R-1,R-6 x N-4 where N-4 is hyperKibler, with vanishing four-form. Supersymmetric warped product dS(5) solutions are then classified; it is shown that all such solutions are generalized M5-brane configurations, for which the transverse space is R x N-4 , and N-4 is a hyperKahler manifold. If the four-form is covariantly constant, then N-4 admits a hyperKahler potential.