  Relatively dominated representations give a common generalization of
geometrically finiteness in rank one on the one hand, and the Anosov condition
which serves as a higher-rank analogue of convex cocompactness on the other.
This note proves three results about these representations.
  Firstly, we remove the quadratic gaps assumption involved in the original
definition. Secondly, we give a characterization using eigenvalue gaps,
providing a relative analogue of a result of Kassel--Potrie for Anosov
representations. Thirdly, we formulate characterizations in terms of singular
value or eigenvalue gaps combined with limit maps, in the spirit of
Gu\'eritaud--Guichard--Kassel--Wienhard for Anosov representations, and use
them to show that inclusion representations of certain groups playing weak
ping-pong and positive representations in the sense of Fock--Goncharov are
relatively dominated.
