Temporal　knowledge　graphs　(TKGs)　are　receiving　increased　attention　due　to　their　time-dependent　properties　and　the　evolving　nature　of　knowledge　over　time.　TKGs　typically　contain　complex　geometric　structures,　such　as　hierarchical,　ring,　and　chain　structures,　which　can　often　be　mixed　together.　However,　embedding　TKGs　into　Euclidean　space,　as　is　typically　done　with　TKG　completion　(TKGC)　models,　presents　a　challenge　when　dealing　with　high-dimensional　nonlinear　data　and　complex　geometric　structures.　To　address　this　issue,　we　propose　a　novel　TKGC　model　called　multicurvature　adaptive　embedding　(MADE).　MADE　models　TKGs　in　multicurvature　spaces,　including　flat　Euclidean　space　(zero　curvature),　hyperbolic　space　(negative　curvature),　and　hyperspherical　space　(positive　curvature),　to　handle　multiple　geometric　structures.　We　assign　different　weights　to　different　curvature　spaces　in　a　data-driven　manner　to　strengthen　the　ideal　curvature　spaces　for　modeling　and　weaken　the　inappropriate　ones.　Additionally,　we　introduce　the　quadruplet　distributor　(QD)　to　assist　the　information　interaction　in　each　geometric　space.　Ultimately,　we　develop　an　innovative　temporal　regularization　to　enhance　the　smoothness　of　timestamp　embeddings　by　strengthening　the　correlation　of　neighboring　timestamps.　Experimental　results　show　that　MADE　outperforms　the　existing　state-of-the-art　TKGC　models.