四維復(fù)歐氏空間的單位球面中的一類浸入環(huán)面.pdf

1、大連理工大學(xué)碩士學(xué)位論文四維復(fù)歐氏空間的單位球面中的一類浸入環(huán)面姓名：鄧?yán)嫔暾垖W(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：侯中華20070622四維復(fù)歐氏空間的單位球面中的—類浸入環(huán)面AtypeoftorusimmersedintotheunitsphereofthefourdimensionalComplexEuclideanSpaceAbstractInthisthesis，wemainlydiscussatypeoftorusimme

2、rsedintotheunitsphereofthefourdimensionalComplexEuclideanSpacewiththeparameterexpression：s：，G，吁)=∽G“，eln)，以G嘻，em)，^(et，em)，■Gt，em))，(a)where售，町)∈p，2，r】【0，2療】，五(1≤k≤4)arepolynomialsoftwovariableswithrealcoefcients，andsati

3、sfyt：lz(∥礦)『2Co)^，lForthepolynomialsoftwovariables，weCallexpressthemby石(工，y)=∑∑％礦y7，A(x，j，k=0I=0A(x，Y)=∑∑％礦Y。，工(x，y=∑∑％∥y。，‘，：(c)=∑∑dzx“Y，where％，％，％，如∈R，1≤|i，，≤玎aleconstantsInthispaperconsideringthefeatureofthemodelsanda

4、pplyingtheFouriertransformation，themovingframemethodandtheexteriordifferentialmethodwefirstobtaintheconstraintconditionequationsofthecoefficientsof五(1≤k≤4)Thenweconcentratetothecasewhenn=1Twocasesaleconsideredtoanalyzeit

5、sexistenceAndthefollowingresultsarcobtained：Theorem231LetSbeatorusparametrizedby(a)，where五(1≤k≤4)aleallpolynomialsoftwovariableswithrealcoefficients，definedby(c)andsatisfyCo)ThenSCan’tbetotallygeodesicwhenn=1“Theorem232L