  In systems above one dimension a continuously degenerate minimum of the
single particle dispersion is realized due to one or a combination of
system-parameters such as lattice structure, isotropic spin-orbit coupling, and
interactions. A unit codimension of the dispersion-minima leads to a divergent
density of states which enhances the effects of interactions, and may lead to
novel states of matter as exemplified by Luttinger liquids in one dimensional
bosonic systems. Here we show that in dilute, homogeneous bosonic systems above
one dimension, weak, spin-independent, inter-particle interactions stabilize a
metallic state at zero temperature in the presence of a curved manifold of
dispersion minima. In this metallic phase the system possesses a quasi
long-range order with non-universal scaling exponents. At a fixed positive
curvature of the manifold, increasing either the dilution or the interaction
strength destabilizes the metallic state towards charge density wave states
that break one or more symmetries. The magnitude of the wave vector of the
dominant charge density wave state is controlled by the product of the mean
density of bosons and the curvature of the manifold. We obtain the zero
temperature phase diagram, and identify the phase boundary.
