子流形與子流形曲率流的相關問題.pdf

1、湖北大學碩士學位論文子流形與子流形曲率流的相關問題姓名：毛井申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：李光漢20090501湖北大學碩士學位論文AbstractThispaperhassolvedthefollowingtwoproblems：(1)ConsideringthecompactpseudoumbilicalsubmanifoldMnwithparallelmeancurvatuevectorintheRiemannianm

2、anifoldN腫p(c)withconstantcurvatureC，andiftheinherentq砼antitiesofMn，K，Q(KandQdenotetheinfimumofsectionalcurvatureandRiccicurvatureineverydirectionateachpointrespectively)，satisfysuit—ableconditions，thenMnmustbeatotallyumb

3、ilicalsubmanifoldofNnp(c)(2)ConsideringanentiregraphM0oversomehyperplanein艫1，whichevolvesinthefollowingway纛=㈨№∽clm。pEMnt0where日(，t)isthemeancnlNatul℃ofMt=Xt(Mn)，砌，t)istheouterunitnormalofMtandClisnonnegativeconstantIfini

4、tialhypersurfaceM0hasboundedsecondfundamentalform，andthenwewillobtaingradientandcurvatureestimatesforagivensuitablecondition(hasrelationshipwiththefamilyofmappingx(，亡))，leadingtolongtimeexistenceoftheflowdefinedasaboveTh

5、elimitinghypersurfaceisstillanentiregraphovertheprescribedhyperplaneKeyWords：Riemannianmanifold；meancurvaturevector；pseudoumbilicalsub—manifolds；totallyumbilicalsubmanifolds；evolutionequation；maximumprinciple；paraboliceq