  A relativistic theory of surficial Love numbers, which characterize the
surface deformation of a body subjected to tidal forces, was initiated by
Damour and Nagar. We revisit this effort in order to extend it, clarify some of
its aspects, and simplify its computational implementation. First, we refine
the definition of surficial Love numbers proposed by Damour and Nagar, and
formulate it directly in terms of the deformed curvature of the body's surface,
a meaningful geometrical quantity. Second, we develop a unified theory of
surficial Love numbers that applies equally well to material bodies and black
holes. Third, we derive a compactness-dependent relation between the surficial
and (electric-type) gravitational Love numbers of a perfect-fluid body, and
show that it reduces to the familiar Newtonian relation when the compactness is
small. And fourth, we simplify the tasks associated with the practical
computation of the surficial and gravitational Love numbers for a material
body.
