Point　clouds　can　capture　the　precise　geometric　information　of　objects　and　scenes,　which　are　an　important　source　of　3D　data　and　one　of　the　most　popular　3D　geometric　data　structures　for　cognitions　in　many　real-world　applications　like　automatic　driving　and　remote　sensing.　However,　due　to　the　influence　of　sensors　and　varieties　of　objects,　the　point　clouds　obtained　by　different　devices　may　suffer　obvious　geometric　changes,　resulting　in　domain　gaps　that　are　prone　to　the　neural　networks　trained　in　one　domain　failing　to　preserve　the　performance　in　other　domains.　In　order　to　alleviate　the　above　problem,　this　paper　proposes　an　unsupervised　domain　adaptation　framework,　named　HO-GSM,　as　the　first　attempt　to　model　high-order　geometric　structures　of　point　clouds.　Firstly,　we　construct　multiple　self-supervised　tasks　to　learn　the　invariant　semantic　and　geometric　features　of　the　source　and　target　domains,　especially　to　capture　the　feature　invariance　of　high-order　geometric　structures　of　point　clouds.　Secondly,　the　discriminative　feature　space　of　target　domain　is　acquired　by　using　contrastive　learning　to　refine　domain　alignment　to　specific　class　level.　Experiments　on　the　PointDA-10　and　GraspNetPC-10　collection　of　datasets　show　that　the　proposed　HO-GSM　can　significantly　outperform　the　state-of-the-art　counterparts.　　©　2020　IEEE.