资源描述：
《gtm 218-lee j.m___introduction to smooth manifolds (draft, 2000)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、INTRODUCTIONTOSMOOTHMANIFOLDSbyJohnM.LeeUniversityofWashingtonDepartmentofMathematicsJohnM.LeeIntroductiontoSmoothManifoldsVersion3.0December31,2000ivJohnM.LeeUniversityofWashingtonDepartmentofMathematicsSeattle,WA98195-4350USAlee@math.washington.eduhttp://www.math.washin
2、gton.edu/~leec2000byJohnM.LeePrefaceThisbookisanintroductorygraduate-leveltextbookonthetheoryofsmoothmanifolds,forstudentswhoalreadyhaveasolidacquaintancewithgeneraltopology,thefundamentalgroup,andcoveringspaces,aswellasbasicundergraduatelinearalgebraandrealanalysis.Itisa
3、naturalsequeltomyearlierbookontopologicalmanifolds[Lee00].Thissubjectisoftencalleddi erentialgeometry."Ihavemostlyavoidedthisterm,however,becauseitappliesmoreproperlytothestudyofsmoothmanifoldsendowedwithsomeextrastructure,suchasaRiemannianmet-ric,asymplecticstructure,aL
4、iegroupstructure,orafoliation,andofthepropertiesthatareinvariantundermapsthatpreservethestructure.Al-thoughIdotreatallofthesesubjectsinthisbook,theyaretreatedmoreasinterestingexamplestowhichtoapplythegeneraltheorythanasobjectsofstudyintheirownright.Astudentwho nishesthisb
5、ookshouldbewellpreparedtogoontostudyanyofthesespecializedsubjectsinmuchgreaterdepth.Thebookisorganizedroughlyasfollows.Chapters1through4aremainlyde nitions.Itisthebaneofthissubjectthattherearesomanyde nitionsthatmustbepiledontopofoneanotherbeforeanythingin-terestingcanbes
6、aid,muchlessproved.Ihavetried,nonetheless,tobringinsigni cantapplicationsasearlyandasoftenaspossible.The rstonecomesattheendofChapter4,whereIshowhowtogeneralizetheclassicaltheoryoflineintegralstomanifolds.Thenextthreechapters,5through7,presentthe rstoffourmajorfoundationa
7、ltheoremsonwhichallofsmoothmanifoldstheoryrests
8、theinversefunctiontheorem
9、andsomeapplicationsofit:tosubmanifoldthe-viPrefaceory,embeddingsofsmoothmanifoldsintoEuclideanspaces,approximationofcontinuousmapsbysmoothones,andquotientsofmanifoldsbygroupactions.Thenextfourchapte
10、rs,8through11,focusontensorsandtensor eldsonmanifolds,andprogressfromRiemannianmetricsthroughdi
