文档介绍：Spinors
Sp ectral Geometry
and
Riemannian Submersions
PETER B
GILKEY y Departmen t of Mathematics
Univ ersit y of Oregon
Eu
gene Or
USA
email
gilk ey
math
uoregon
edu
JOHN V
LEAHY Departmen t of Mathematics
Univ ersit y of Oregon
Eugene
Or
USA
email
leah y
darkwing
u oregon
edu
JEONGHYEONG P ARK z Departmen t of Mathematics
Honam Univ ersit y
Kw ang ju South Korea email
jhpark
honam
h onam
ac
kr
y Researc h partially supp orted b y the NSF
USA
Researc h partially supp orted b y the GAR C
z Researc h partially supp orted b yK OSEF
and BSRI
the
Korean Ministry of Education
i
Preface
These lecture notes app eared as Lecture Notes Series Num ber
intheRe
searc h Institute of Mathematics
Global Analysis Researc h Cen ter
Seoul National
Univ ersit y
Seoul
Korea
Professor Sang Mo on Kim
who is Director of
GAR C
has kindly giv en his p ermission for us to p ost them on the EMIS w eb
serv er
W e note that with the p ermission of the GAR C
these notes ha v e b
pletely rewritten and expanded to form Chapter F our of the b o ok Sp ectral Ge
ometry
Riemannian Submersions
and the Gromo v
La wson Conjecture
b y Gilk ey
Leah y and P ark
This b o ok is exp ected to app ear in summer
from
CR C press
W e are are grateful to the EMIS for making these Lecture Notes a v ailable on
the w orld wide w eb
ii
Con ten ts
In tro duction
Chapter One
Riemannian Submersions
In tro duction
Mean curv ature and in tegrabilit y tensors
Normalization of lo cal co ordinates