  We discuss alternative homogeneous electron gas systems in which a finite
number $n$ of electrons are confined to a $D$-dimensional sphere. We derive the
first few terms of the high-density ($r_s\to0$, where $r_s$ is the Seitz
radius) energy expansions for these systems and show that, in the thermodynamic
limit ($n\to\infty$), these terms become identical to those of $D$-dimensional
jellium.
