實(shí)復(fù)空間形式中的子流形.pdf

1、華南師范大學(xué)碩士學(xué)位論文實(shí)復(fù)空間形式中的子流形姓名：王霞申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：李世杰2003.6.1AbstractThispaper∞Rsigtsoftwoparts，Inthefirstpart，weconsiderthecompacttotallyrealpseudoumbilicalsubmaaifoldsM“thathavenongerop8rMIe[aermMizedm#atl￡lt[va￡urev黜￡∞

2、in㈣彗程sp耗eforms蠡銣奶褥Asaresult，(i)LetK(x)bethefunctionassigntoeachpoint茁ofMtheinfintmumofthesectiona|curvatureso￡囂atthatponi％琵辯囊≥sa≤isf／esK髦嘉黼譬十4艫)～鍍譬赫謄，thenMistotallyumbilical(ii)Let0缸)bethefunctlonassigntoeachpoint霉ofMthe

3、infinlmumoftheRicei錨蝴熬瑤裙媾M舔￡殛瞎爹。撼≈囂鴦#》satisfiesQ≥弘一2》幫4H2)一纛瓦一thenMistotallyumbilical(i11)Let∥bethe8quarelength0fthesecond氛穗螺煉麟溉璉if囂satiresg墨警拜囂拶，thenM話瓣舔跨umbilical(iv)ifthescalarcurvaturepsatisfies∥乏擊(3雌2—5扎)(謄4H2)一蕊the

4、n材istotalkvumbilical、where璉isthec鞣stantmeanCllrVture。Inthesecondpart，玳investigacethecompactsubmanifoldsMwiththeparallelisoperimetricsectionin臻erealspaceforms彤’觸andprovethatifthere漱a璐藤瓣isoperimetriesectionOnM，andthesectio

5、nalcurvatureofMisalwaysgreaterthanzero。thenMiscontainedinahypersphere；andget漱theGausseurvatureofthecempactsurfacesMwithconstantmeancurvatnreinconstantcurvaturespaceR4(G)isalwaysgreaterthan2elo，thenMisatotallygeo￡lesicsur

6、f勰撼鑫sphere。where囂丞京露瓣孓metricf強(qiáng)MmeansqunitnormalvectorfielddefinedgloballyonMwithA矗(黲；c觸8ta眥。Keywords：coraplexspaceform，毫。噬孥rams毽溉滟轂她懿蛩tlm■billcalsubmanlfolds，pseudoumbilicalsnbmanifolds，parallelnormalizedmeancurvaturevec