  A regularization procedure developed in [1] for the integral curvature
invariants on manifolds with conical singularities is generalized to the case
of squashed cones. In general, the squashed conical singularities do not have
rotational O(2) symmetry in a subspace orthogonal to a singular surface
$\Sigma$ so that the surface is allowed to have extrinsic curvatures. A new
feature of the squashed conical singularities is that the surface terms in the
integral invariants, in the limit of small angle deficit, now depend also on
the extrinsic curvatures of $\Sigma$. A case of invariants which are quadratic
polynomials of the Riemann curvature is elaborated in different dimensions and
applied to several problems related to entanglement entropy. The results are in
complete agreement with computations of the logarithmic terms in entanglement
entropy of 4D conformal theories [2]. Among other applications of the suggested
method are logarithmic terms in entanglement entropy of non-conformal theories
and a holographic formula for entanglement entropy in theories with gravity
duals.
