Being　able　to　estimate　monocular　depth　for　spherical　panoramas　is　of　fundamental　importance　in　3D　scene　perception.　However,　spherical　distortion　severely　limits　the　effectiveness　of　vanilla　convolutions.　To　push　the　envelope　of　accuracy,　recent　approaches　attempt　to　utilize　Tangent　projection　(TP)　to　estimate　the　depth　of　360(degrees)　images.　Yet,　these　methods　still　suffer　from　discrepancies　and　inconsistencies　among　patch-wise　tangent　images,　as　well　as　the　lack　of　accurate　ground　truth　depth　maps　under　a　supervised　fashion.　In　this　paper,　we　propose　a　geometry-aware　self-supervised　360(degrees)　image　depth　estimation　methodology　that　explores　the　complementary　advantages　of　TP　and　Equirectangular　projection　(ERP)　by　an　asymmetric　dual-domain　collaborative　learning　strategy.　Especially,　we　first　develop　a　lightweight　asymmetric　dual-domain　depth　estimation　network,　which　enables　to　aggregate　depth-related　features　from　a　single　TP　domain,　and　then　produce　depth　distributions　of　the　TP　and　ERP　domains　via　collaborative　learning.　This　effectively　mitigates　stitching　artifacts　and　preserves　fine　details　in　depth　inference　without　overspending　model　parameters.　In　addition,　a　frequent-spatial　feature　concentration　module　is　devised　to　simultaneously　capture　non-local　Fourier　features　and　local　spatial　features,　such　that　facilitating　the　efficient　exploration　of　monocular　depth　cues.　Moreover,　we　introduce　a　geometric　structural　alignment　module　to　further　improve　geometric　structural　consistency　among　tangent　images.　Extensive　experiments　illustrate　that　our　designed　approach　outperforms　existing　self-supervised　360(degrees)　depth　estimation　methods　on　three　publicly　available　benchmark　datasets.