Construction of a complete negatively curved singular riemannian foliation

Let (M, g) be a complete Riemannian manifold and G be a closed (connected) subgroup of the group of isometries of M. Then the union ${MM}$ of all principal orbits is an open dense subset of M and the quotient map ${MM} longrightarrow {BB} := {MM}/G$ becomes a Riemannian submersion for the restriction of g to ${MM}$ which gives the quotient metric on ${BB}$. Namely, B is a singular (complete) Riemannian space such that $partialB$ consists of non-principal orbits.

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