Leibniz quantum compact metric spaces
We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the commutant of the quantum tori in the regular representation, when this group is endowed with a natural length function.
Latrémolière, Frédéric, "Curved Noncommutative Tori as Leibniz Quantum Compact Metric Space" (2015). Mathematics Preprint Series. Paper 1.