Real hyperbolic on the outside, complex hyperbolic on the inside

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A spherical CR structure on the complement of the figure eight knot with discrete holonomy (2005, methodology): “The only construction of such a structure on a 3-manifold (which is not a circle bundle) previous to this work is essentially for the Whitehead link and other manifolds obtained from it by Dehn surgery in [ S1 , S2].”
New non-arithmetic complex hyperbolic lattices (2014, methodology): “An important example of such a groupwas studied in [41], where Schwartz gave a fundamental domain for a group generated by complex reflections I1, I2, I3 of order 2 with pairwise products of order 4 and such that I1 I2 I3 I2 has order 7.”
COMPLEX HYPERBOLIC GEOMETRY OF THE FIGURE EIGHT KNOT (2013, background): “Indeed, Schwartz showed in [17] that the Whitehead link complement admits a uniformizable spherical CR structure, and in [18] he found an example of a closed hyperbolic manifold that arises as the boundary of a complex hyperbolic surface.”
Traces in Complex Hyperbolic Triangle Groups (2004, methodology): “Another example of explicit parameterisation is the parameterisation of (4,4,4)-groups in [ 15 ].”