We　consider　the　stabilization　of　the　transmission　wave/plate　equation　with　variable　coefficients　and　a　general　transmission　boundary.　By　virtue　of　the　Riemannian　geometric　approach,　we　obtain　some　stability　results　for　nonlinear　feedbacks　acting　on　the　regions　under　suitable　geometric　conditions.　(C)　2017　Elsevier　Inc.　All　rights　reserved.