超球面的特征及曲面無窮小等距.pdf

1、江西師范大學(xué)碩士學(xué)位論文超球面的特征及曲面無窮小等距姓名：聞家君申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：陳撫良20070501AbstractThisdissertationisconsistoftWOpartsInthefirstpart，wediscussedthecharacterizationsofHypersphereinEuclideanspace，summarizedsometheoremsaboutthecharact

2、erizationsofHypersphere，weobtainedsomeequivalenttheoremsonthecharacterizationsofHypersphereinE3，E4，E5，E6andgivensimpleproofgeneralizedseveraltheoremsTheoremA：LetMCZE”1beacompacthypersurfacewithanorthogonalsystemof1inesof

3、curvatureSuppose：①tO，i=1，2，，撐：②theboundaryaMofMconsistsofumbilicalpoints：③墨=c1(H=C)：ThenMiSapartofahypersphereTheoremB：LetMcE”1beacompacthypersurfacewithanorthogonalsystemof1inesofcurvatureSuppose：①電0i=l，2，，n：②％=c2(‰=∥)：

4、ThenMisapartofahypersphere●TheoremC：LetMcE4州beacompacthypersurfaCeithanorthogonalsystemof1inesofcurvatureSuppose：①置O，i=1，2，，n：(多theboundaryOMofMconsiStSofumbilicalpoints：③thereis，onM，∑Ldt，。0，Z：M哼Rbeingpositivefunctionssu

5、chthatthematrix‰)《柚M)ispositivelysemi—definiteforpairwisedifferent=f，J’i，J’2，：，Li，％=厶厶一Z，七≠，；6址=2∽厶)；ThenMisapartof“ahypersphere’’Inthesecondpart，theconceptionofInfinitesimalIsometryofSurfacesinE“isintroduced，wegeneraliz

6、edsomeresultsaboutInfinitesimalIsometryinE3，E4，E5bytheoryofpartialdifferentialequation(solutionofpartialdifferentialequations)andobtainedatheoremaboutInfinitesimalIsometryofSurfacesinE”TheoremD：Let胍D—E”，DcR2aboundeddomai

7、n，beasurface療：M斗Ⅳ(吖)iSasection，formII(‰，)ispositivelydefiniteform∈M，vectorn。andmeancurvaturevectoriSnotorthogonalatmLetViSInfinitesimalIsometryofM，匕belongtothevectorspacespannedbyL(肘)and／／mform∈MIfm∈aM，圪orthogonalto乙(M)t