Generalized Symmetric Spaces

  • PDF / 8,142,035 Bytes
  • 198 Pages / 461 x 684 pts Page_size
  • 62 Downloads / 222 Views

DOWNLOAD

REPORT


805 OId~ich Kowalski

Generalized Symmetric Spaces



Springer-Verlag Berlin Heidelberg New York 1980

Author OId~ich Kowalski Department of Mathematical Analysis Faculty of Mathematics and Physics Charles University, Sokolovska 83 186 00 Prague/Czechoslovakia

AMS Subject Classifications (1980): 15A21, 17 B40, 22 E25, 53C05, 53C20, 53C30, 53C35, 53C55 ISBN 3-540-10002-4 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-387-10002-4 Springer-Verlag NewYork Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under £354 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1980 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210

P R E F A C E

In

this

symmetric and

the

ved.

these

sic

group

some

of any We

spaces theory

theories

one

such

restrictions to

or

spaees

and

6

The

present

an

meaning

this

same

ductive

book

part

does

not

(why symmetric

plaee

to

pay

past).

A

good

analogue

has

in

to The not been

the

a

the

a - yet

the

ba-

briefly

exposition

is a

a

to

we

do

not

the the

of

the

group-theoretical

direc-

"generalized a

sym-

concepts

(usually

a

a

Lie

elosed necessarily and

of

geometrical

are

affine

"generalized

symmetric

space".

concept

geometrical

G

involutive). purely

concepts

triplet

sub~roup

group-theoretical

more

Riemannian

part

denoting

not new

of a

niekname

"generalized

replace

theory than

as

precise

basic

and

the

only H

which give

by

of

expression

used

i the

of theory

detailed of

included, in

too. Further,

are

to

the

the

the

the which

only

concept

book

is

of

the

study

of

spite

of

or and

devoted

ordinary

theory

O.Loos?)

of

of

to

other

to

the

eigenvalues

of

the

may

a

re-

an

affine

as

a spe-

Note

the

book

is n o t

our

great

that the

in

generalized

have parti-

spaces

is

progress

symmetric in

right the

symmetries.

considerable

interest

of which

spaces;

a

refe-

the

men

pseudo-Riemannian

faet

stimulate

also

also is n o t

questions

of'pseudo-Riemannian

(See

spaces

and

(this

symmetric

symmetrie of

symmetric

exceptional

E.Cartan

generalized in

theory

S.Helgason

spaces

deal

theory made

contain

tribute

[CPI]~[CP2],[CW]) tions,

G

duplicate

to

also

into on

refer

our

rather (For

far~

group,

to

space"

rences

cular~

part

algebras.

Lie

space

simulate

space.)

The

no

a

we

homogeneous

reductive

a

group-theoretical

expression

spirit,

as

usually

tries

Riemannian

the

In

invol-

([WoG],[Gr])

restrictions

connection

So

of

author

to

Lie

is

automor