Table Of ContentProgress in Mathematics
Takushiro Ochiai
Toshiki Mabuchi
Yoshiaki Maeda
Junjiro Noguchi
Alan Weinstein
Editors
In Memory of Professor Shoshichi
Kobayashi
Progress in Mathematics
Volume 308
Series Editors
Hyman Bass, University of Michigan, Ann Arbor, USA
Jiang-Hua Lu, The University of Hong Kong, Hong Kong SAR, China
Joseph Oesterlé, Université Pierre et Marie Curie, Paris, France
Yuri Tschinkel, Courant Institute of Mathematical Sciences, New York, USA
More information about this series at http://www.springer.com/series/4848
Takushiro Ochiai • Toshiki Mabuchi • Yoshiaki Maeda
Junjiro Noguchi • Alan Weinstein
Editors
Geometry and Analysis
on Manifolds
In Memory of Professor Shoshichi Kobayashi
Editors
Takushiro Ochiai Toshiki Mabuchi
Graduate School of Mathematical Sciences Department of Mathematics
The University of Tokyo Graduate School of Sciences
Tokyo, Japan Osaka University
Osaka, Japan
Yoshiaki Maeda
Tohoku Forum for Creativity Junjiro Noguchi
Tohoku University Graduate School of Mathematical Sciences
Yokohama, Japan The University of Tokyo
Tokyo, Japan
Alan Weinstein
Department of Mathematics
University of California at Berkeley
Berkeley, CA, USA
ISSN 0743-1643 ISSN 2296-505X (electronic)
Progress in Mathematics
ISBN 978-3-319-11522-1 ISBN 978-3-319-11523-8 (eBook)
DOI 10.1007/978-3-319-11523-8
Library of Congress Control Number: 2015932660
Mathematics Subject Classification (2010): 53-06, 32Q45, 53C15, 32Q15, 32Q20, 58C10
Springer Cham Heidelberg New York Dordrecht London
© Springer International Publishing Switzerland 2015
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microfilms or in any other physical way, and transmission or information
storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now
known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this book
are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the
editors give a warranty, express or implied, with respect to the material contained herein or for any errors
or omissions that may have been made.
Printed on acid-free paper
Springer International Publishing AG Switzerland is part of Springer Science+Business Media
(www.springer.com)
Contents
Preface .................................................................. vii
Part 1: About Shoshichi Kobayashi
T. Ochiai
In Memory of Professor Shoshichi Kobayashi ........................ 3
H.-H. Wu
Events Surrounding the Birth of the Kobayashi Metric .............. 13
H. Kobayashi
Academic Genealogy of Shoshichi Kobayashi and
Individuals Who Influenced Him .................................... 17
Part 2: Algebraic Geometry and Complex Analysis
J. Merker
Algebraic Differential Equations for Entire Holomorphic
Curves in Projective Hypersurfaces of General Type:
Optimal Lower Degree Bound ....................................... 41
J. Noguchi
Kobayashi Hyperbolicity and Lang’s Conjecture ..................... 143
T. Ohsawa
A Lemma on Hartogs Function and Application to
Levi Flat Hypersurfaces in Hopf Surfaces ............................ 153
H. Tsuji
On the Extremal Measure on a Complex Manifold .................. 159
P. Vojta
A Lang Exceptional Set for Integral Points .......................... 177
K. Yamanoi
Kobayashi Hyperbolicity and Higher-dimensional
Nevanlinna Theory ................................................. 209
vi Contents
J.-H. Yang
Geometry and Arithmetic on the Siegel–Jacobi Space ............... 275
S.-T. Yau
On the Pseudonorm Project of Birational Classification
of Algebraic Varieties ............................................... 327
Part 3: Differential Geometry
A. Futaki
The Weighted Laplacians on Real and Complex Metric
Measure Spaces ..................................................... 343
K. Hasegawa and Y. Kamishima
Locally Conformally Ka¨hler Structures on Homogeneous Spaces ..... 353
N. Hitchin
A Note on Vanishing Theorems ..................................... 373
G.R. Jensen
Dupin Hypersurfaces in Lie Sphere Geometry ....................... 383
T. Mabuchi
The Donaldson–Futaki Invariant for Sequences of
Test Configurations ................................................. 395
T. Mabuchi and Y. Nitta
Strong K-stability and Asymptotic Chow-stability ................... 405
Y. Maeda and S. Rosenberg
Traces and Characteristic Classes in Infinite Dimensions ............ 413
R. Miyaoka
Moment Map Description of the Cartan–Mu¨nzner Polynomials
of Degree Four ...................................................... 437
U. Hertrich-Jeromin and Y. Suyama
Ribaucour Pairs Corresponding to Dual Pairs of
Conformally Flat Hypersurfaces ..................................... 449
M.S. Tanaka
Geometry of Symmetric R-spaces ................................... 471
Preface
Prof. Shoshichi Kobayashi was a recognized international leader in differential
geometry and complex geometry. As detailed below, throughout a career lasting
over five decades, he contributed crucial new ideas which are still fundamental in
these researchareas, particularly within complex geometry.
Prof.Kobayashi’searlywork contributed to a wide rangeof topics in differ-
ential geometry, for example through his well-known work on the study of trans-
formationgroupsandontheFrankelconjecture,whichcharacterizedcomplexpro-
jective spaces. In complex geometry, his work on Hermitian-Einstein holomorphic
vector bundles led to the so-called Kobayashi–Hitchincorrespondence.
Themostwell-knownmathematicalobjectbearinghisnameistheKobayashi
pseudometric, which he introduced in 1967. This has become an essential tool for
thestudyofmappingsbetweencomplexmanifolds.Heidentifiedacrucialproperty
of“good”spaces,whichhe calledhyperbolic, inthis theory,andwhichin recogni-
tion of this fundamental insight are now known as Kobayashi hyperbolic spaces.
Perhapsmostimportantly,hisbooks,especiallythetwovolume“Foundations
of Differential Geometry” with Katsumi Nomizu, have taught differential geome-
try and complex geometry to generations of students and other researchers. His
writing is known for its succinctness and clarity, and the book commonly known
as Kobayashi–Nomizuhas been in publication for over 50 years.
Over the course of his long career, Prof. Kobayashi produced a most im-
pressive mathematical legacy in the form of 35 Ph.D. students, a long list of con-
tributions to differential geometry, and many influential monographs. As part of
his interest in the dissemination of mathematics, he contributed immensely to
thecommunicationbetweenUSandJapanesemathematicians.Hegreatlyenjoyed
mathematical discussions with young researchers, and with great warmth always
encouragedthem.Prof.ShoshichiKobayashilivesonintheformofhismagnificent
mathematical legacy and our memories of a wonderful man.
We are very grateful to Professor Shoshichi Kobayashi for his distinguished
contributions to differential geometry and complex geometry, and we are pleased
tobeabletopublishavolumededicatedtohimconsistingofinvitedcontributions
from his PhD students, co-workers and colleagues working on topics close to his
researchareas. All papers are refereed to the standards of an excellent journal.
Finally,wethankthe editorsatBirkh¨auserfortheirconstantencouragement
for this publication.
The editors Takushiro Ochiai (chair)
Toshiki Mabuchi
Yoshiaki Maeda
Junjiro Noguchi
Alan Weinstein
Shoshichi Kobayashi
Part 1
About Shoshichi Kobayashi
