Transcription of Notes on Difierential Geometry - CMU
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Notes on Difierential Geometry - CMU
NotesonDi erentialGeometrywithspecialemphasisonsur facesinR3 MarkusDesernoMay 3, 2004 Department of ChemistryandBiochemistry, UCLA,LosAngeles,CA90095-1569,USAMax-Plan ck-Institutf ur Polymerforschung,Ackermannweg 10,55128 Mainz,GermanyThesenotesareanattemptto summarizesomeof thekeymathe-maticalaspectsof di erentialgeometry, as theyapplyin particularto thegeometryof surfacesinR3. Thefocusis notonmathematicalrigorbutratheroncollect ingsomebitsandpiecesof theverypow-erfulmachineryof manifoldsand\post-Newtoniancalculus".Eve nthoughtheultimategoalof eleganceis a completecoordinatefreedescription,thisgo alis farfrombeingachievedhere|notbecausesuch a descriptiondoes notexistyet,butbecausetheauthoris farto thegeometricaspectsaretakenfromFrankel's book[9],onwhich thesenotesrelyheavily. For \classical"di erentialgeometryof curves andsurfacesKreyszigbook[14] hasalsobeentakenas a presentationvariesquitea greatdetail,othersareonlytoucheduponquic kly, mostlywiththeintent to indicateintowhich directiona particularsubjectmight be thetheory of nitions.
Notes on Difierential Geometry with special emphasis on surfaces in R3 Markus Deserno May 3, 2004 Department of Chemistry and Biochemistry, UCLA, Los Angeles, CA 90095-1569, USA
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