關(guān)于仿射超曲面仿射完備和歐氏完備的注記.pdf

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??‰€aμn?;’??μ?:ê?Xμê??úO?¤?mμ2015c4AthesissubmittedtoZhengzhouUniversityforthedegreeofMasterThenotesaboutanecompleteandEuclideancompleteofanehypersurfacesBy:DongLuoSupervisor:Prof.Ze

2、junHuDisciplines:ScienceSpeciality:PureMathematicsDepartment:SchoolofMathematicsandStatisticsCompletionDate:April,2015學位論文原創(chuàng)性聲明本人鄭重聲明：所呈交的學位論文，是本人在導師的指導下，獨立進行研究所取得的成果.除文中己經(jīng)注明引用的內(nèi)容外，本論文不包含任何其他個人或集體己經(jīng)發(fā)表或撰寫過的科研成果.對本文的研究作出重要貢獻的個人和集體,均已在文中以明確方式標明.本聲明的法律責任由本人承擔.，學位

3、論文作者：貧奮、?*W年命/日學位論文使用授權(quán)聲明本人在導師指導下完成的論文及相關(guān)的職務(wù)作品，知識產(chǎn)權(quán)歸屬鄭州大學.根據(jù)鄭州大學有關(guān)保留、使用學位論文的規(guī)定，同意學校保留或向國家有關(guān)部門或機構(gòu)送交論文的復印件和電子版，允許論文被查閱和借閱；本人揆權(quán)鄭州大學可以將本學位論文的全部或部分編入有關(guān)數(shù)據(jù)庫進行檢索，可以釆用影印、縮印或者其他復制手段保存論文和匯編本學位論文.本人離校后發(fā)表、使用學位論文或與該學位論文直接相關(guān)的學術(shù)論文或成果時,第一署名單位仍然為鄭州大學.保密論文在解密后應(yīng)遵守此規(guī)定.學位論文作者：裔、y/

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5、曰á?????????￡Yt¤???￡Yt¤'X"y2Xeì?(JμRn′??à?§f′??3t1w!??à?ê§??f?”???M§XJ?ü??à????M'uBlaschkeYtGPick?CtJ(B)k.§Kiù6/(M;G)…=M'uRn+1??pYt"t?(JéoS????￡?[!¤k'??‰??[y2"?uxú￡¤D3??^?e'u?V?.?￥?aCalabi??1?ü?y2±9T.Sasaki'uCalabi??

6、1ü?y2,dt?(?,·??á=Calabic?????#y2"'…c:????,?￥,??,?,Calabi??"iAbstractInthispaper,westudytherelationbetweentheane(metric)completenessandtheEuclidean(metric)completenessonequianehypersurfaces.Themainresultisasfollows:LetRnbeaconvexdomainandf:!

7、Risasmoothandstronglyconvexfunction.LetMbethegraphhypersurfaceoff.AssumethatthePickinvariantJ(B)ofthelocallystronglyconvexanehypersurfaceMwithrespecttotheBlaschkemetricGisboundedfromabove.ThentheRiemannianmanifold(M;G)iscompleteifandonlyifMisEuclideancomplet

8、e,i.e.MiscompletewithrespecttoitsinducedmetricfromtheEuclideanspaceRn+1.OurproofoftheaboveresultisadetailedclaricationtooneclaimmadebyProfessorAn-MinLi.Fromtheaboveresult,andcombiningwithS.Y.ChengandS.T.Yau'sprooftotherstpartoftheCalabiconjectureontheclassi

9、cationofanecomplete,hyperbolicanehyperspheres(undertheadditionalconditionofEuclideancompleteness),andalsoT.Sasaki'sproofoftheCalabiconjecture'ssecondpart,weobtainimmediatelyanewandcomp