  We analyze the central dark-matter (DM) content of \sim 4,500 massive (M*
\gsim 10^{10} Msun), low-redshift (z<0.1), early-type galaxies (ETGs), with
high-quality ugrizYJHK photometry and optical spectroscopy from SDSS and
UKIDSS. We estimate the "central" fraction of DM within the K-band effective
radius, \Re, using spherically symmetric isotropic galaxy models. We discuss
the role of systematics. The main results of the present work are the
following: (1) DM fractions increase systematically with both structural
parameters and mass proxies, as in previous studies, and decrease with central
stellar density. 2) All correlations involving DM fractions are caused by two
fundamental ones with galaxy effective radius and central velocity dispersion.
These correlations are independent of each other, so that ETGs populate a
central-DM plane (DMP), i.e. a correlation among fraction of total-to-stellar
mass, effective radius, and velocity dispersion, whose scatter along the
total-to-stellar mass axis amounts to \sim 0.15 dex. (3) In general, under the
assumption of an isothermal or a constant M/L profile for the total mass
distribution, a Chabrier IMF is favoured with respect to a bottom-heavier
Salpeter IMF, as the latter produces negative (i.e. unphysical) DM fractions
for more than 50% of the galaxies in our sample. For a Chabrier IMF, the DM
estimates agree with \LambdaCDM toy-galaxy models based on contracted DM-halo
density profiles. We also find agreement with predictions from hydrodynamical
simulations. (4) The central DM content of ETGs does not depend significantly
on the environment where galaxies reside, with group and field ETGs having
similar DM trends. (Abridged)
