關于一類不定復射影空間中全實類空子流形若干問題研究.pdf

1、關于一類不定復射影空間中全實類空子流形若干問題的研究鄭家耀(安徽師范大學數(shù)學計算機科學學院，安徽，蕪湖241000)安徽師范大學碩士學位論文二零一五年四月OntheStudyofTotallyRealSpacelikeSubmanifoldsofaClassofIndefiniteComplexProjectiveSpaceAbstractIndefinitecomplexprojectivespaceanditstotallyreal

2、spacelikesubmanifoldsareofsupremeimptanceinthestudyofdifferentiablegeometry.Inthisthesiswemainlystudythetotallyrealspacelikesubmanifoldsofaspecialclassofindefinitecomplexprojectivespace.Underthebasicassumptionthatthesect

3、ionalcurvatureisconstantwegetseveralconditionsftheexistenceofmaximalimmersionsfromthetotallyrealspacelikesubmanifoldsandthesubmanifolds’acterbycalculating.BesideswealsoconstitutesomeRicciinqualitiesandCheninqualitiesonth

4、etotallyrealspacelikesubmanifolds.Thisthesisismadeupof3chapters:Inthe1stchapterwemainlyintroducethedevelopmentbackgroundandsituationofthedifferentiablegeometryintroducetheprovenanceandtheresearchsignificanceoftheindefini

5、tecomplexprojectivespaceprovidethemainknowledgewhichweuseandthemainwkofthisthesis.Inthe2ndchapterwemainlyusethemovingframemethodtoresearchthetotallyrealspacelikesubmanifoldsofaclassofindefinitecomplexprojectivespaceindet

6、ail.Firstlywegetanecessaryconditionftheexistenceofmaximalimmersionsfromatotallyrealspacelike2harmonicsubmanifoldhavingameancurvaturevectintotheindefinitecomplexprojectivespacebycalculatingandusingtheCauchyinequality.Then

7、wereachthatatotallyrealandtotallyumbilicalspacelikesubmanifoldcan’tbeflatbystudyingthepositionofumbilicalnmalvectbundle.Finallywealsoshowthatonestyleoftotallyrealpseudoumbilicalspacelikesubmanifoldbeingflatmustbemaximal.