Contact Manifolds in Riemannian Geometry

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509 David E. Blair

Contact Manifolds in Riemannian Geometry

Springer-Verlag Berlin. Heidelberg. New York 1976

Author David Ervin Blair Department of Mathematics Michigan State University East Lansing, Michigan 48824 USA

Library of Congress Cataloging in Publication Data

Blair, David E 19/+OContact manifolds in Riemannanian geometry. (Lecture notes in mathematics ; 509) "A slightly expanded version of the authorts lectures at the University of Strasbourg and the University of Liverpool during the academic year 197~-75 9 Bibliography: p. Includes index. i. Geometry, Riemannian. 2. Riemarmian manifolds. I. Title. If, Series: Lecture notes in mathematics (Berlin) ; 509. QA3.L28 no. 509 cQA649~ 510'.8s c516' .373~ 76-3757

AMS Subject Classifications (1970): 53-02, 53C15, 5 3 C 2 5 ISBN 3-540-07626-3 ISBN 0-38?-0?626-3

Springer-Verlag Berlin 9Heidelberg 9New York Springer-Verlag New York Heidelberg 9 9Berlin

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 w 54 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. 9 bySpringer-Verlag Berlin 9Heidelberg 1976 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.

PREFACE

These author's

notes

lectures

University

during

of c o n t a c t

provided

in the

The two large manifolds

later

classes

fibration

including

sphere bundles.

eralizations

have r e c e i v e d

manifolds

is m a d e these

here to give

classes

distribution

The

examples

considerable class

insight

spheres and

has not.

Finally

This

metric

a

distribution,

In fact the m a x i m u m is half

the d i m e n s i o n

is d i s c u s s e d

in C h a p t e r integral

form.

in C h a p t e r VI we p r o v e

flat a s s o c i a t e d

of b o t h

determines

the c o n t a c t

submanifold

space

as c o n t a c t

IV and VII).

integrable.

of a S a s a k i a n

its gen-

into the g e o m e t r y

called

and

An a t t e m p t

and C h a p t e r V deals w i t h r e c e n t w o r k on the

submanifolds

of c o n t a c t

attention

form on a contact m a n i f o l d

distribution.

some

of theBoothby-

former class

in Chapters

of an integral

of the c o n t a c t

to the s u b j e c t w i t h

circle b u n d l e s

or subbundle,

these

lectures.

latter

some

is far from b e i n g

dimension

III

the

(chiefly

The c o n t a c t

which

but

1974-75.

to the audiences,

the o d d - d i m e n s i o n a l

the t a n g e n t

metric

year

and the

from the R i e m a n n i a n

of c l a s s i c a l

are the p r i n c i p a l

of the

of S t r a s b o u r g

manifolds

an i n t r o d u c t i o n

recent work given

version

the a c a d e m i c

of v i e w was not w e l l k n o w n

lectures

Wan