Riemannian Geometry - P.Petersen.pdf

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Graduate Texts in Mathematics
Editorial Board
S. Axler
K.A. Ribet
Graduate Texts in Mathematics
1T AKEUTI /Z ARING . Introduction to
Axiomatic Set Theory. 2nd ed.
2O XTOBY . Measure and Category. 2nd ed.
3 CHAEFER . Topological Vector Spaces.
2nd ed.
4H ILTON /S TAMMBACH . A Course in
Homological Algebra. 2nd ed.
5M AC L ANE . Categories for the Working
Mathematician. 2nd ed.
6H UGHES /P IPER . Projective Planes.
7 J.-P. S ERRE . A Course in Arithmetic.
8T AKEUTI /Z ARING . Axiomatic Set Theory.
9H UMPHREYS . Introduction to Lie
Algebras and Representation Theory.
34
S PITZER . Principles of Random Walk.
2nd ed.
35
A LEXANDER /W ERMER . Several Complex
Variables and Banach Algebras. 3rd ed.
36
K ELLEY /N AMIOKA et al. Linear
Topological Spaces.
37
M ONK . Mathematical Logic.
38
G RAUERT /F RITZSCHE . Several Complex
Variables.
A RVESON . An Invitation to C * -Algebras.
39
40
K EMENY /S NELL /K NAPP . Denumerable
Markov Chains. 2nd ed.
41
A POSTOL . Modular Functions and
Dirichlet Series in Number Theory.
2nd ed.
10
C OHEN . A Course in Simple Homotopy
Theory.
42
J.-P. S ERRE . Linear Representations of
Finite Groups.
11
C ONWAY . Functions of One Complex
Variable I. 2nd ed.
43
G ILLMAN /J ERISON . Rings of
Continuous Functions.
12
B EALS . Advanced Mathematical Analysis.
13
A NDERSON /F ULLER . Rings and
Categories of Modules. 2nd ed.
44
K ENDIG . Elementary Algebraic
Geometry.
14
G OLUBITSKY /G UILLEMIN . Stable
Mappings and Their Singularities.
45
L OÈVE . Probability Theory I. 4th ed.
46
L OÈVE . Probability Theory II. 4th ed.
15
B ERBERIAN . Lectures in Functional
Analysis and Operator Theory.
47
M OISE . Geometric Topology in
Dimensions 2 and 3.
16
W INTER . The Structure of Fields.
48
S ACHS /W U . General Relativity for
Mathematicians.
17
R OSENBLATT . Random Processes. 2nd ed.
18
H ALMOS . Measure Theory.
49
G RUENBERG /W EIR . Linear Geometry.
2nd ed.
19
H ALMOS . A Hilbert Space Problem
Book. 2nd ed.
50
E DWARDS . Fermat’s Last Theorem.
20
H USEMOLLER . Fibre Bundles. 3rd ed.
51
K LINGENBERG . A Course in Differential
Geometry.
21
H UMPHREYS . Linear Algebraic Groups.
22
B ARNES /M ACK . An Algebraic
Introduction to Mathematical Logic.
52
H ARTSHORNE . Algebraic Geometry.
53
M ANIN . A Course in Mathematical Logic.
23
G REUB . Linear Algebra. 4th ed.
54
G RAVER /W ATKINS . Combinatorics with
Emphasis on the Theory of Graphs.
24
H OLMES . Geometric Functional
Analysis and Its Applications.
55
B ROWN /P EARCY . Introduction to
Operator Theory I: Elements of
Functional Analysis.
25
H EWITT /S TROMBERG . Real and Abstract
Analysis.
26
M ANES . Algebraic Theories.
56
M ASSEY . Algebraic Topology: An
Introduction.
27
K ELLEY . General Topology.
28
Z ARISKI /S AMUEL . Commutative
Algebra. Vol. I.
57
C ROWELL /F OX . Introduction to Knot
Theory.
29
Z ARISKI /S AMUEL . Commutative
Algebra. Vol. II.
58
K OBLITZ . p -adic Numbers, p -adic
Analysis, and Zeta-Functions. 2nd ed.
30
J ACOBSON . Lectures in Abstract Algebra
I. Basic Concepts.
59
L ANG . Cyclotomic Fields.
60
A RNOLD . Mathematical Methods in
Classical Mechanics. 2nd ed.
31
J ACOBSON . Lectures in Abstract Algebra
II. Linear Algebra.
61
W HITEHEAD . Elements of Homotopy
Theory.
32
J ACOBSON . Lectures in Abstract Algebra
III. Theory of Fields and Galois
Theory.
62
K ARGAPOLOV /M ERIZJAKOV .
Fundamentals of the Theory of Groups.
33
H IRSCH . Differential Topology.
63
B OLLOBAS . Graph Theory.
(continued after index)
Peter Petersen
Riemannian Geometry
Second Edition
 
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Peter Petersen
Department of Mathematics
University of California, Los Angeles
Los Angeles, CA 90095-1555
USA
petersen@math.ucla.edu
Editorial Board:
S. Axler
Department of Mathematics
San Francisco State University
San Francisco, CA 94132
USA
axler@sfsu.edu
K.A. Ribet
Department of Mathematics
University of California, Berkeley
Berkeley, CA 94720-3840
USA
ribet@math.berkeley.edu
Mathematics Subject Classification (2000): 53-01
Library of Congress Control Number: 2006923825
ISBN-10: 0-387-29246-2
e-ISBN 0-387-29403-1
ISBN-13: 978-0387-29246-5
Printed on acid-free paper.
© 2006 Springer Science +Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the
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they are subject to proprietary rights.
Printed in the United States of America.
(MVY)
987654321
springer.com

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