  Nuclear systems under constraints, with high degrees of symmetries and/or
collectivities may be considered as moving effectively in spaces with reduced
spatial dimensions. We first derive analytical expressions for the nucleon
specific energy $E_0(\rho)$, pressure $P_0(\rho)$, incompressibility
coefficient $K_0(\rho)$ and skewness coefficient $J_0(\rho)$ of symmetric
nucleonic matter (SNM), the quadratic symmetry energy $E_{\rm{sym}}(\rho)$, its
slope parameter $L(\rho)$ and curvature coefficient $K_{\rm{sym}}(\rho)$ as
well as the fourth-order symmetry energy $E_{\rm{sym,4}}(\rho)$ of neutron-rich
matter in general $d$ spatial dimensions (abbreviated as "$d$D") in terms of
the isoscalar and isovector parts of the isospin-dependent single-nucleon
potential according to the generalized Hugenholtz-Van Hove (HVH) theorem. The
equation of state (EOS) of nuclear matter in $d$D can be linked to that in the
conventional 3-dimensional (3D) space by the $\epsilon$-expansion which is a
perturbative approach successfully used previously in treating second-order
phase transitions and related critical phenomena and more recently in studying
the EOS of cold atoms. The $\epsilon$-expansion of nuclear EOS in $d$D based on
a reference dimension $d_{\rm{f}}=d-\epsilon$ is shown to be effective with
$-1\lesssim\epsilon\lesssim1$ starting from $1\lesssim d_{\rm{f}}\lesssim3$ in
comparison with the exact expressions derived using the HVH theorem. Moreover,
the EOS of SNM (with/without considering its potential part) is found to be
reduced (enhanced) in lower (higher) dimensions, indicating in particular that
the many-nucleon system tends to be deeper bounded but saturate at higher
densities in spaces with lower dimensions. The links between the EOSs in 3D and
$d$D spaces from the $\epsilon$-expansion provide new perspectives to the EOS
of neutron-rich matter.
