We study the Grassmann geometry of surfaces when the ambient space is a 3-dimensional non-unimodular Lie group with left invariant metric. This work together with our previous papers yield a complete classification of Grassmann geometry of orbit type in all 3-dimensional homogeneous spaces.
"Grassmann geometry on the 3-dimensional non-unimodular Lie groups." Hokkaido Math. J. 48 (2) 385 - 406, June 2019. https://doi.org/10.14492/hokmj/1562810516