文档介绍：A
B B
-
VOLUMEII
A
A
ComprehensiveIntroduction
to
DIFFERENTIALGEOMETRY
VOLUMETWO
SecondEdition
MICHAELSPIVAK
,tIne.
COPYRIGHT© 1975,1979 BY MICHAEL SPIVAK
ALL RIGHTSRESERVED
ISBN0-914098-88-8
ClothSet, Vols. ,5 ISBN 0-914098-82-9
ClothSet, Vols. 1-5ISBN 0-914098-83-7
LibraryofCongress Card Catalog Number 78-71771
PUBLISHOR PERISH,INC.
HOUSTON,TEXAS (.)
InJapan distributed exclusively by
PANY LTD
TOKYO,JAPAN
Printedinthe United States ofAmerica
For
Harry
Josh
and
Marc
PREFACE
Somewhatto mysurp rise, thesecond volu meof thesenotes came ou t more
orless as I hadpl anned. Actually ,that state mentis only half true , foronly
halfthe mate rialwhich I hadpla nnedto itewrhas co meout at al l;the res t
willhave fit toin toVo lumeIII, whic h Ipra y willbe the las t . ThisVo lume
ends ata suitablestopping point , when wehave fi nallygotten to the fa nciest
definitionofa connection,but hardlybegunto st artsp outingth eorems. A
glanceat the Ta bleof Co ntentswill show tha t thesemi -historicalpath pro­
misedin Vo lumeI reallyhas bee n followed. Themo stdec isiveen counterswith
classicaldif ferentialgeo ur in Chapters 3 nd a 4, wh ichare di vided
intopart s ;so meparts present the class icalpape rs, nd aot herpar tsexp lain
them. Itis possible toget th roughthe no tes withoutre adingany of the cla s­
sicalworks the mselves, butthe easy way out mis ses ll a th e fun. The students
inmy cl assfo undGa ussexciti ng,and whi lethey fou ndRi emann'sown wo rds
bewildering, theywere am azedwhen they learned what Rie mannhad be entr yingto
say . Toread Gau ss, oneshould get hold of th e RavenPress trans lationof
Gauss'Gen eralInves tigationsofCur vedSur faces. Thereare two selec tionsfrom
Riemann, both ofwh ichhave be enin cludedin th e notes. Asfar as I know, no
translationofthe Latin paper in Chapter 4Chas previ ously beenava ilable.
Sincemo stof th