The X-ray transform on 2-step nilpotent Lie groups of higher rank
  We prove injectivity and a support theorem for the X-ray transform on $2$-step nilpotent Lie groups with many totally geodesic $2$-dimensional flats. The result follows from a general reduction principle for manifolds with uniformly escaping geodesics. 
Norbert Peyerimhoff, Evangelia Samiou
math.DG