We study the dynamics of unipotent flows on frame bundles of hyperbolic manifolds of infinite volume. We prove that they are topologically transitive and that the natural invariant measure, the so-called Burger–Roblin measure, is ergodic, as soon as the geodesic flow admits a finite measure of maximal entropy, and this entropy is strictly greater than the codimension of the unipotent flow inside the maximal unipotent flow. The latter result generalizes a theorem of Mohammadi and Oh.
"On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds." Duke Math. J. 168 (4) 697 - 747, 15 March 2019. https://doi.org/10.1215/00127094-2018-0050