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
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