不可約黎曼對(duì)稱空間的曲率估計(jì)及其應(yīng)用.pdf

1、、廠955282仫旦大學(xué)學(xué)校代碼：10246學(xué)號(hào)：0210]8034博士學(xué)位論文不可約黎曼對(duì)稱空間的曲率估計(jì)及其應(yīng)用院系(所)：數(shù)學(xué)科學(xué)學(xué)院專姓業(yè)：名：基礎(chǔ)數(shù)學(xué)劉旭勝指導(dǎo)教師：忻元龍教授完成El期：2005年10月15日CUR：VATUREESTIMATESFORSYMMETRJCSPACESWITHAPPLIC觚‘IoNSLiuXusheng(majoredinbasicmathematics)DirectedbyProfYSnYua

2、n—longAccordingtotheclassificationsofRiemanniansymmetricspaces，wetransformtheCaftansubalgebraswithmaximalcompactpartintotheCaxtansubalgebraswithmaximalnoncompactpartbyusingtheCayLeytransformationWe舀vetheboundsofsectional

3、curvatttreforallirreduciblePdemaaniansymmetricspacesFromtheclassificationsofthemaydInalsubsystemsofabstractrootsystems，wecalculatethesvaluesofpartialpositivityforallirreduciblesymmetricspacesAsallapplicationwe百vethefollo

4、wingLiouvilletypetheorem：Theorem01LetMbe∞eoltheirreduciblesymmetricspacesolnoncompacttypeinthefollowingcases，SL(n，R)／sD(n)，n≥4；SU(2n)／sp(n)；SU(p，q)／S(％％)，Pq≥4；SOo(P，q)／SOb)SO(q)，，0rr=1，Pq≥4，，orr1，Pq≥6，herer=min(p，q)；SO(2

5、n)／u(n)，n≥3；sp(n，R)／u(n)，n≥3；卻0，q)／Sp(p)X3p(q)；E1，EII，EIII，E1UEEEyj，Ey，J，EyJJj，EIX，F(xiàn)I，F(xiàn)IIandGLet／beaharmonicmapfromMintoanyRiemannianman咖ldwithmoderatedivergentenergy，then，hastobeconstantForexceptionalgeometry，wegivethef