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1、AnnalsofMathematicsMinimalTwo-SpheresandtheTopologyofManifoldswithPositiveCurvatureonTotallyIsotropicTwo-PlanesAuthor(s):MarioJ.MicallefandJohnDouglasMooreReviewedwork(s):Source:TheAnnalsofMathematics,SecondSeries,Vol.127,No.1(Jan.,1988),pp.199-227Publishedby:AnnalsofMathematicsStableURL:ht
2、tp://www.jstor.org/stable/1971420.Accessed:30/12/201104:01YouruseoftheJSTORarchiveindicatesyouracceptanceoftheTerms&ConditionsofUse,availableat.http://www.jstor.org/page/info/about/policies/terms.jspJSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuildu
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4、hematics.http://www.jstor.orgAnnalsofMathematics,127(1988),199-227Minimaltwo-spheresandthetopologyofmanifoldswithpositivecurvatureontotallyisotropictwo-planesByMARioJ.MICALLEF*andJOHNDOUGLASMOORE**TableofContents1.Introductionandstatementofresults2.Theindexofharmonictwo-spheresinM3.Critical
5、pointsoflowindexforthea-energy4.Theexistenceofharmonictwo-spheresoflowindex5.Stableminimaltwo-spheresinmanifoldsofnonnegativecurvatureReferences1.IntroductionandstatementofresultsTherehasbeenmuchinterestamongdifferentialgeometersinfindingrelationshipsbetweencurvatureandtopologyofRiemannianm
6、anifolds.Forthemostpart,effortshavebeendirectedtowardsunderstandingtheimplicationsofpositiveornegativesectionalcurvature,Riccicurvature,orscalarcurvature,butthereareotherhypothesesonthecurvaturewhichalsodeserveinvestigation.Inthisarticle,wewillconsiderthetopologicalimplicationsofanewcurvatu
7、reassumption,positivecurvatureontotallyisotropictwo-planes,andwewillproveviatheSacks-Uhlenbecktheoryofminimaltwo-spheresthatacompactsimplyconnectedRiemannianmanifoldofdimensionatleastfour,withpositivecurva-tureontotallyisotropictwo-planesishomeomorphicto
