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We construct solutions of an Einstein-Yang-Mills system including acosmological constant in 4+n space-time dimensions, where the n-dimensionalmanifold associated with the extra dimensions is taken to be Ricci flat.Assuming the matter and metric fields to be independent of the n extracoordinates, a spherical symmetric Ansatz for the fields leads to a set ofcoupled ordinary differential equations. We find that for n > 1 only solutionswith either one non-zero Higgs field or with all Higgs fields constant and zerogauge fields exist. We give the analytic solutions available in this model.These are ``embedded'' abelian solutions with a diverging size of the manifoldassociated with the extra n dimensions. Depending on the choice of parameters,these latter solutions either represent naked singularities or they possess asingle horizon.  We also present solutions of the effective 4-dimensionalEinstein-Yang-Mills-Higgs-dilaton model, where the higher dimensionalcosmological constant induces a Liouville-type potential. The solutions arenon-abelian solutions with diverging Higgs fields, which exist only up to amaximal value of the cosmological constant.Comment: 13 Tex-pages, 2 eps-figures; discussions changed; some points  clarifie

Spherically symmetric solutions of a (4 + n )-dimensional Einstein–Yang–Mills model with cosmological constant