關(guān)于一類不定復(fù)射影空間中全實(shí)類空子流形若干問(wèn)題研究.pdf

1、關(guān)于一類不定復(fù)射影空間中全實(shí)類空子流形若干問(wèn)題的研究鄭家耀(安徽師范大學(xué)數(shù)學(xué)計(jì)算機(jī)科學(xué)學(xué)院，安徽，蕪湖241000)安徽師范大學(xué)碩士學(xué)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.