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Eleven-dimensional supergravity admits non-supersymmetric solutions of theform AdS(5)xM(6) where M(6) is a positive Kahler-Einstein space. We show thatthe necessary and sufficient condition for such solutions to be stable againstlinearized bosonic supergravity perturbations can be expressed as a conditionon the spectrum of the Laplacian acting on (1,1)-forms on M(6). For M(6)=CP(3),this condition is satisfied, although there are scalars saturating theBreitenlohner-Freedman bound. If M(6) is a product S(2)xM(4) (where M(4) isKahler-Einstein) then there is an instability if M(4) has a continuousisometry. We show that a potential non-perturbative instability due to 5-branenucleation does not occur. The bosonic Kaluza-Klein spectrum is determined interms of eigenvalues of operators on M(6).

On the stability and spectrum of non-supersymmetric AdS(5) solutions of M-theory compactified on Kahler-Einstein spaces