黎曼流形間復(fù)合映射伸縮度的估計(jì).pdf

1、中國(guó)科學(xué)技術(shù)大學(xué)碩士學(xué)位論文黎曼流形間復(fù)合映射伸縮度的估計(jì)姓名：李淑華申請(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：彭家貴2001.5.1，／Abstract：ThedilatationofthemapsbetweentheRiemannianmanifoldsisanimportantgeometricinvariant，whichiscloselyrelatedwithtopologyItisanimportantproblemtost

2、udytheserelationshipsindifferentialgeometryandtopologyThispaperpresentsadiscussiononthetopologicalcomplexityofamap，：S”_S“anditsgeometricalcomplexityAsweknowitisnaturaltomeasuregeometricalcomplexityofthemapfbyitsdilatatio

3、nThetopologicalcomplexityofthemapfmaybemeasuredbyitshomotopyclassortheBrouwerdegree(whentheBrouwerdegreemakessense)Howdoesthemap’StopologicalcomplexityeffectitsgeometricalcomplexityThispapersummarizessomefundamentalconcl

4、usionsabouttheproblemmentionedaboveAlsowepresentsadiscussiononthedilatationofcompositionmappingGenerallyletM，N，HbeRiemannianmanifolds，ifthereexitf：M_N，gr：NH，thena(a。f)≤占(∞6(f)Moreover，Roitbergconjecturedin[7】that8(a。f)=占

5、(盯)60，=2占(f)，atleastif仃isoneoftheHopfclassesHoweverin1998，ProfessorPengChiakueiandTangZizhoupointedoutin【4】thatRoitbergconjecturedidnotholdon巧】(s2)WepointoutthatRoitbergconjecturedoesnotholdon石，(s4)and石，s(S。)eitherThethi