  The Abelian Higgs model with or without external particles is considered in
curved space. Using the dual transformation, we rewrite the model in terms of
dual gauge fields and derive the Bogomol'nyi-type bound. We examine
cylindrically symmetric solutions to Einstein equations and the first-order
Bogomol'nyi equations, and find vortex solutions and vortex-particle composites
which lie on the spatial manifold with global geometry described by a cylinder
asymptotically or a two sphere in addition to the well-known cone.
