Current Developments in Differential Geometry and its Related Fields: Proceedings of the 4th International Colloquium on Differential Geometry and its Related Fields

256 Pages·2015·6.405 MB·English

by  Toshiaki Adachi, Hideya Hashimoto, Milen J Hristov (eds.)

9748_9789814713788_tp.indd 1 29/9/15 5:47 pm
May2,2013 14:6 BC:8831-ProbabilityandStatisticalTheory PST˙ws
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
9748_9789814713788_tp.indd 2 29/9/15 5:47 pm
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Cover images:
(front) Sokolski Monastery of the Assumption, Gabrovo
(back) The road “Alexander Stanboliyski” to the museum, Veliko Tarnovo
Photographed by T. Adachi
CURRENT DEVELOPMENTS IN DIFFERENTIAL GEOMETRY AND
ITS RELATED FIELDS
Proceedings of the 4th International Colloquium on Differential Geometry
and its Related Fields
Copyright © 2016 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,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance
Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy
is not required from the publisher.
ISBN 978-981-4713-78-8
Desk Editor: Lai Fun Kwong
Cover Designer: Doris Zhenghua Yu
Printed in Singapore
LaiFun - Current Developments.indd 1 28/8/2015 1:54:20 PM
September14,2015 14:11 BookCode: 9748–CurrentDevelopmentsinDifferentialGeometry ws-procs9x6˙ICDG2014 pagev
v
PREFACE
This volume containspaperswrittenby some ofthe participantsinthe 4th
International Colloquium on Differential Geometry and its Related Fields
(ICDG2014) which was held at Europe Hall in Rectral Building, St. Cyril
andSt.MethodiusUniversityofVelikoTarnovo,Bulgaria,duringtheperiod
of8–12September,2014. Withwarmhospitalityandassistanceofthestaff
of the faculty of Mathematics and Informatics, Veliko Tarnovo University,
participants discussed quite freely and exchanged their ideas.
Thearticlesinthisvolumearemainlydevotedtothestudyofsomegeo-
metricstructuresonmanifoldsandtheirdiscretizations. Thesecoverrecent
developments on Einstein metrics on Lie groups, Einstein-Weyl structures
on3-dimensionalmanifolds,quaternionicCRmanifolds,exceptionalgeom-
etry, totally geodesic surfaces in symmetric spaces, mathematical physics,
lightlikesubmanifolds,complexstatisticalmanifolds,newtreatmentofsur-
facesinaEuclidean3-space,andLaplaciansofgraphs. Wehopethisvolume
will provide a broad overview of differential geometry and its relationship
to other fields in mathematics and physics.
Thisacademicprogramisbasedontheagreementofacademicexchange
and cooperation between the University of Veliko Tarnovo and Nagoya In-
stituteofTechnology. WegladlyhadyoungBulgariannewcomers. Wehope
ourprogramwillencourageyoungscientistsfromBulgaria,Japanandsome
other countries. Unfortunately, we have to make a solemn note. Professor
BagreliyaBorisova,theformerVicerectoroninternationalactivitiesofUni-
versity of Veliko Tarnovo, passed away on December 17, 2013. We would
like to pay tribute to her and her achievements.
We gratefully acknowledge a financial support for the conference activ-
ities by NITech Grant for Global Initiative Projects, Nagoya Institute of
Technology. We appreciateverymuchthe scientificreviewerswhoreadthe
articlescarefullyandgavemanyimportantsuggestionstoauthors. Finally,
we express our hearty thanks to the local staff, especially Professor Paskal
N. Piperkov, for their hospitality.
The Editors
17 May, 2015
May2,2013 14:6 BC:8831-ProbabilityandStatisticalTheory PST˙ws
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
August27,2015 9:16 BookCode: 9748–CurrentDevelopmentsinDifferentialGeometry ws-procs9x6˙ICDG2014 pagevii
vii
The 4th International Colloquium
on Differential Geometry and its Related Fields
8–12 September, 2014 – Veliko Tarnovo,Bulgaria
ORGANIZING COMMITTEE
T. Adachi – Nagoya Institute of Technology, Nagoya,Japan
S. H. Bouyuklieva – St. Cyril and St. Methodius University of
Veliko Tarnovo, Veliko Tarnovo,Bulgaria
H. Hashimoto – Meijo University, Nagoya,Japan
M. J. Hristov – St. Cyril and St. Methodius University of
Veliko Tarnovo, Veliko Tarnovo,Bulgaria
SCIENTIFIC ADVISORY COMMITTEE
G. Ganchev – Bulgarian Academy of Sciences, Sofia, Bulgaria
K. Sekigawa – Niigata University, Niigata, Japan
T. Sunada – Meiji University, Tokyo, Japan
May2,2013 14:6 BC:8831-ProbabilityandStatisticalTheory PST˙ws
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
September14,2015 14:11 BookCode: 9748–CurrentDevelopmentsinDifferentialGeometry ws-procs9x6˙ICDG2014 pageix
ix
PRESENTATIONS
at Europe Hall, Rectral Building,
St.CyrilandSt.MethodiusUniversity
1. Yusuke Sakane (Osaka Univ.),
New homogeneous Einstein metrics on compact simple Lie groups
2. Galya Nakova (Univ. Veliko Tarnovo),
Curvature properties of some lightlike hypersurfaces
of almost complex manifolds with Norden metric
3. Fuminori Nakata (Fukushima Univ.),
Circle invariant indefinite Einstein-Weyl structures
and the twistor correspondence
4. Krassen Iliev & Milen Hristov (Univ. Veliko Tarnovo),
On the Laplace-matrix calculus
5. Toshiaki Adachi (Nagoya Inst. Tech.),
K¨ahler graphs
— Discrete models of manifolds equipped with magnetic fields —
6. Yarmamat Tursun (Nagoya Inst. Tech.),
Laplacians for K¨ahler graphs
7. Hiroshi Matsuzoe (Nagoya Inst. Tech.),
Geometry of deformed exponential families
8. Nikolay Ivanov (Univ. Veliko Tarnovo),
Noncommutative Instantons
9. Hiroyuki Kamada (Miyagi Univ. of Education),
Geometric structure modeled on a real hypersurface
in a quaternionic manifold
10. Misa Ohashi (Nagoya Inst. Tech.),
A method of determinig the SO(7)-invariants for curves
in ImO by their G -invariants
2
11. Milen Hristov & Victoria Bencheva (Univ. Veliko Tarnovo),
On the differential geometry of Laplace-transformed curves