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1、漫谈微分几何、多复变函数与代数几何（Differentialgeometry,functionsofcomplexvariableandalgebraicgeometry）Differentialgeometryandtensoranalysis,developedwiththedevelopmentofdifferentialgeometry,arethebasictoolsformasteringgeneralrelativity.Becausegeneralrelativity'ssuccess,toalwaysobscuredifferentialge
2、ometryhasbecomeoneofthecentraldisciplineofmathematics.Sincetheinventionofdifferentialcalculus,thebirthofdifferentialgeometrywasborn.ButtheworkofEuler,ClairautandMongereallymadedifferentialgeometryanindependentdiscipline.Intheworkofgeodesy,Eulerhasgraduallyobtainedimportantresearch,a
3、ndobtainedthefamousEulerformulaforthecalculationofnormalcurvature.TheClairautcurveofthecurvatureandtorsion,Mongepublished"analysisisappliedtothegeometryofthelooseleafpaper",theimportantpropertiesofcurvesandsurfacesarerepresentedbydifferentialequations,whichmakesthedevelopmentofclass
4、icaldifferentialgeometrytoreachapeak.Gaussinthestudyofgeodesic,throughcomplicatedcalculation,in1827foundtwomaincurvaturesurfacesanditsproductintheperipheryoftheEuclideanshapeofthespacenotonlydependsonitsfirstfundamentalform,theresultisGaussproudlycalledthewonderfultheorem,createdfro
5、mtheintrinsicgeometry.Thefreesurfaceofspacefromtheperiphery,thesurfaceitselfasaspacetostudy.In1854,Riemannmadethehypothesisaboutgeometricfoundation,andextendedtheintrinsicgeometryofGaussin2dimensionalcurvedsurface,thusdevelopingn-dimensionalRiemanngeometry,withthedevelopmentofcomple
6、xfunctions.Agroupofexcellentmathematiciansextendedtheresearchobjectsofdifferentialgeometrytocomplexmanifoldsandextendedthemtothecomplexanalyticspacetheoryincludingsingularities.Eachstepofdifferentialgeometryfacesnotonlythedeepeningofknowledge,butalsothecontinuousexpansionofthefieldo
7、fknowledge.Here,differentialgeometryandcomplexfunctions,Liegrouptheory,algebraicgeometry,andPDEallinteractprofoundlywithoneanother.Mathematicsisconstantlydividingandblendingwitheachother.Byshiningthecharminggloryandthedifferentialgeometricfunctiontheoryofseveralcomplexvariables,unit
8、circleandtheupperha
