Topics on Real and Complex Singularities

212 Pages·2014·3.841 MB·English

by  Satoshi Koike, Toshizumi Fukui, Laurentiu Paunescu, Adam Harri, Alexander Isaev

TOPICS REAL
ON AND
COMPLEX SINGULARITIES
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TOPICS REAL
ON AND
COMPLEX SINGULARITIES
Proceedings of the 4th Japanese–Australian Workshop (JARCS4)
Kobe, Japan 22 – 25 November 2011
Editors
Satoshi Koike
Hyogo University of Teacher Education, Japan
Toshizumi Fukui
Saitama University, Japan
Laurentiu Paunescu
University of Sydney, Australia
Adam Harris
University of New England, Australia
Alexander Isaev
Australian National University, Australia
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
9115_9789814596039_tp.indd 2 27/1/14 11:45 am
Published by
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
TOPICS ON REAL AND COMPLEX SINGULARITIES
Proceedings of the 4th Japanese–Australian Workshop (JARCS4)
Copyright © 2014 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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ISBN 978-981-4596-03-9
Printed in Singapore
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BC:9115-JARCS4Proceeding Topics
v
Preface
The fourth Japanese-Australian Workshop on Real and Complex Sin-
gularities (JARCS4 KOBE 2011) was held at the Kobe Satellite of Hyogo
University of Teacher Education during the period 22-25 November, 2011.
There were 31 participants from Australia and Japan.
The Australian and Japanese Singularity Theory specialists have built
up a strong research relationship in the past three decades. For instance,
the blow-analytic theory introduced by Tzee-Char Kuo in Australia has
been intensively developed in Japan. In addition, a lot of joint works by
researchersofbothcountrieshavebeenestablishedinseveraltopicsrelated
to real and complex singularities.
The present volume consists mainly of the texts of the invited talks of
the workshop. Some of them are joint works of Australians and Japanese.
Thisvolumecontainsoriginalarticlesonrealandcomplexsingularities,
topology of differentiable maps, openings of differentiable map-germs, the
relationshipbetween free divisors and holonomic systems, effective compu-
tational method of invariantsof singularities,the applicationofsingularity
theory to differential geometry, the deformation theory of CR structures
and differential equations with singular points. In these articles some im-
portant new notions for characterizations of singularities are introduced,
and several new results are presented. New approaches to classical topics
and new computational methods of singularities are also presented.
We would like to thank the contributors for their cooperation. All the
articlesinthisvolumehavebeenverycarefullyrefereed.Wewouldalsolike
to thank the referees for taking time to read and give a lot of comments
again and again.
The workshop was supported by the Grant-in-Aid for Scientific Re-
searches
No. 23244008(Investigator: Osamu Saeki),
No. 22340030(Investigator: Goo Ishikawa),
No. 23540099(Investigator: Kimio Miyajima),
No. 21540054(Investigator: Shuzo Izumi),
No. 23540087(Investigator: Satoshi Koike)
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of the Ministry of Education, Culture, Sports, Science and Technology
(MEXT) of Japan, and Hyogo University of Teacher Education. We ac-
knowledge the support.
18 September 2013
Satoshi Koike
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Organizing Committees
of the fourth Japanese-AustralianWorkshop on
Real and Complex Singularities
Satoshi Koike (Chairman) – Hyogo University of Teacher Education,
Japan
Toshizumi Fukui – Saitama University, Japan
Laurentiu Paunescu – University of Sydney, Australia
Adam Harris – University of New England, Australia
Alexander Isaev – Australian National University, Australia
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List of Participants
Takao Akahori (Hyogo University, Japan)
Kana Ando (Chiba University, Japan)
Takuo Fukuda (Nihon University, Japan)
Toshizumi Fukui (Saitama University, Japan)
Hirofumi Hagi (Hyogo University of Teacher Education, Japan)
Adam Harris (University of New England, Australia)
Jonathan Hillman (University of Sydney, Australia)
Goo Ishikawa (Hokkaido University, Japan)
Shuzo Izumi (Kinki University, Japan)
Shigeyasu Kamiya (Okayama University of Science, Japan)
Yoshihiro Kawazoe (Hyogo University of Teacher Education, Japan)
Yumiko Kitagawa (Oita National College of Technology, Japan)
Naoki Kitazawa (Tokyo Institute of Technology, Japan)
Mahito Kobayashi (Akita University, Japan)
Satoshi Koike (Hyogo University of Teacher Education, Japan)
Yutaka Matsui (Kinki University, Japan)
Kimio Miyajima (Kagoshima University, Japan)
Masayuki Nishioka (Kyushu University, Japan)
Masao Ogawa (Hyogo University of Teacher Education, Japan)
Mutsuo Oka (Tokyo University of Science, Japan)
Tomohiro Okuma (Yamagata University, Japan)
Laurentiu Paunescu (University of Sydney, Australia)
Osamu Saeki (Kyushu University, Japan)
JiroSekiguchi(TokyoUniversityofAgricultureandTechnology,Japan)
Ryuhei Shigematsu (Hyogo University of Teacher Education, Japan)
Masahiro Shiota (Nagoya University, Japan)
Shinichi Tajima (Tsukuba University, Japan)
Kiyoshi Takeuchi (Tsukuba University, Japan)
Takahiro Yamamoto (Kyushu Sangyo University, Japan)
Wataru Yukuno (Hokkaido University, Japan)
Ruibin Zhang (University of Sydney, Australia)
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Contents
Preface v
Organizing Committees vii
List of Participants viii
On the CR Hamiltonian flows and CR Yamabe problem 1
T. Akahori
An example of the reduction of a single ordinary differential
equation to a system, and the restricted Fuchsian relation 13
K. Ando
Fronts of weighted cones 31
T. Fukui and M. Hasegawa
Involutive deformations of the regular part of a normal surface 51
A. Harris and K. Miyajima
Connected components of regular fibers of differentiable maps 61
J. T. Hiratuka and O. Saeki
The reconstruction and recognition problems for
homogeneous hypersurface singularities 75
A. V. Isaev
Openings of differentiable map-germs and unfoldings 87
G. Ishikawa
Non concentration of curvature near singular points of two
variable analytic functions 115
S. Koike, T.-C. Kuo and L. Paunescu