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简介:InthisarticlewestudyholomorphicisometriesofthePoincar'ediskintoboundedsymmetricdomains.EarlierwesolvedtheproblemofanalyticcontinuationofgermsofholomorphicmapsbetweenboundeddomainswhichareisometriesuptonormalizingconstantswithrespecttotheBergmanmetric,showinginparticularthatthegraphV0ofanygermofholomorphicisometryofthePoincar'ediskΔintoanirreducibleboundedsymmetricdomainΩ€CNinitsHarish-Chandrarealizationmustextendtoanaffine-algebraicsubvarietyVC×CN=CN+1,andthattheirreduciblecomponentofV∩(Δ×Ω)containingV0isthegraphofaproperholomorphicisometricembeddingF:Δ→Ω.Inthisarticlewestudyholomorphicisometricembeddingswhichareasymptoticallygeodesicatageneralboundarypointb∈Δ.Startingwiththestructuralequationforholomor-phicisometriesarisingfromtheGaussequation,weobtainbycovariantdifferentiationanidentityrelatingcertainholomorphicbisectionalcurvaturestotheboundarybehaviorofthesecondfundamentalformσoftheholomorphicisometricembedding.Usingthenonpositivityofholomorphicbisectionalcurvaturesonaboundedsymmetricdomain,weprovethatσmustvanishatageneralboundarypointeithertotheorder1ortotheorder21,calledaholomorphicisometryofthefirstresp.secondkind.Wedealwithspecialcasesofnon-standardholomorphicisometricembeddingsofsuchmaps,showingthattheymustbeasymptoticallytotallygeodesicatageneralboundarypointandinfactofthefirstkindwheneverthetargetdomainisaCartesianproductofcomplexunitballs.WealsostudytheboundarybehaviorofanexampleofholomorphicisometricembeddingfromthePoincar'ediskintoaSiegelupperhalf-planebyanexplicitdeterminationoftheboundarybehaviorofholomorphicsectionalcurvaturesinthedirectionstangenttotheembeddedPoincar'edisk,showingthatthemapisindeedasymptoticallytotallygeodesicatageneralboundarypointandofthefirstkind.Fo
简介:在BCK—代数中引进左映射和在BCI—代数中引进弱左映射,并探讨它们的性质。主要结果是:如果X是BCK—代数,Y是正定关联BCK—代数,则所有X到Y的左映射的集合也构成正定关联BCI—代数;如果X是BCI—代数,Y是弱正定关联BCI—代数,则所有X到Y的弱左映射的集合也构成弱正定关联BCI—代数。这推广了文(1)与(2)的结果。