Proceedings of the 8th International Workshop on Complex Structures and Vector Fields Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk Proceedings of the 8th International Workshop on Complex Structures and Vector Fields Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics Institute of Mathematics and Informatics, Bulgaria 21 – 26 August 2006 Editors Stancho Dimiev Bulgarian Academy of Sciences, Bulgaria Kouei Sekigawa Niigata University, Japan World Scientific N E W J E R S E Y • L O N D O N • S I N G A P O R E • B E I J I N G • S H A N G H A I • H O N G K O N G • TA I P E I • C H E N N A I 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. TOPICS IN CONTEMPORARY DIFFERENTIAL GEOMETRY, COMPLEX ANALYSIS AND MATHEMATICAL PHYSICS Proceedings of the 8th International Workshop on Complex Structures and Vector Fields Copyright © 2007 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-13 978-981-270-790-1 ISBN-10 981-270-790-5 Printed in Singapore. ZhangJi - Topics in contemporary.pmd 1 4/26/2007, 2:21 PM April24,2007 17:34 WSPC-ProceedingsTrimSize:9inx6in pcsvf2006 v PREFACE This book is the Proceedings of the 8th International Workshop on Complex Structures and Vector Fields held at Bulgarian Academy of Sci- ences, Institute of Mathematics and Informatics (Sofia) from August 21 to August 2, 2006. The first Workshop was held at the same place on 1992. We are aiming at the higher achievement of the studies of current top- ics in Complex Analysis,DifferentialGeometry, MathematicalPhysicsand also of the intermediate ones among them including their applications. It isnotable thatmanynew specialistsinMathematicalPhysicsattendedthe present Workshop besides regular participants in the previous Workshops and also that a new tendency to expand our subject matters is adopted in thepresentWorkshop,andplacesespeciallyemphasesonthefurtherdevel- opment of the studies in Differential Geometry, Complex Analysis, Partial Differential Equations and Integrable System, and also on the expansion of the research areas including new ones in Mathematical Physics in the forthcoming Workshops. This book is dedicated to the memory of three distinguished scientists, Professor Shigeru Ishihara who is regarded as a teacher of many Japanese participants, Professor Shozo Koshi who was an active participant of the Workshop, and Professor Sawa Manoff who was an active participant of the Workshop and also made much effort for the development of the same Workshop. TheeditorsexpresstheirdeepestgratitudetoProfessorT.Oguroforhis outstanding co-operation and efforts in the arrangements of this volume. Editors April24,2007 17:34 WSPC-ProceedingsTrimSize:9inx6in pcsvf2006 TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk April24,2007 17:34 WSPC-ProceedingsTrimSize:9inx6in pcsvf2006 vii THE 8TH INTERNATIONAL WORKSHOP ON COMPLEX STRUCTURES AND VECTOR FIELDS 21-26 August 2006, Sofia – Bulgaria ORGANIZING COMMITTEE S. Dimiev (Chairman) – IMI, Sofia, Bulgaria St. Donev – INRNE, Sofia, Bulgaria V. Gerdjikov – INRNE, Sofia, Bulgaria B. Iliev – INRNE, Sofia, Bulgaria R. Lazov – IMI, Sofia, Bulgaria SCIENTIFIC COMMITTEE V. Georgiev (Chairman) — Pisa, Itary S. Dimiev (Chairman) — Bulgaria, Bulgaria D. Alekseevski — Hull, UK K. Sekigawa — Niigata, Japan H. Hashimoto — Nagoya,Japan T. Adachi — Nagoya,Japan S. Maeda — Matsue, Japan Y. Mathsushita — Shiga, Japan S. Marchiafawa — Rome, Italy M. Pontecorvo — Rome, Italy V. Rostov — Nice, France A. Sergeev — Moscow, Russia O. Mushkarov — Sofia, Bulgaria J. Davidov — Sofia, Bulgaria G. Ganchev — Sofia, Bulgaria I. Pestov — Dubna, Russia St. Donev — Sofia, Bulgaria V. Gerdjikov — Sofia, Bulgaria B. Iliev — Sofia, Bulgaria R. Lazov — Sofia, Bulgaria April24,2007 17:34 WSPC-ProceedingsTrimSize:9inx6in pcsvf2006 viii CONTRIBUTED COMMUNICATIONS 1. Yasuo Matsushita Almost K¨ahler-Einsteinstructures on 8-dimensionalWalker manifolds 2. Peter Popivanov On the hypoellipticity of complex valued vector fields 3. Toshiaki Adachi Killing helices on a complex projective space and canonical magnetic fields on geodesic spheres 4. Vestislav Apostolov GeneralizedKa¨hlermanifolds,commutingcomplexstructuresandsplit tangent bundles 5. Rossen Dandoloff Anholonomy of a moving space curve and the Schro¨dinger equation 6. Hideya Hashimoto On almost Hermitian structures of 6-dimensional submanifolds in the octonions 7. Norio Ejiri Complex submanifolds and Lagrangian submanifolds associated with minimal surfaces in tori 8. Julian Lawrinowicz Clusters and fractals in mathematics and physics 9. Vladimir Georgiev Nonexistence ofnonzeroresonancesfor Schro¨dingeroperatorswith sin- gular perturbation 10. Vladimir Gerdjikov Hamiltonian aspects of soliton equations with deep reductions 11. Tihomir Valchev B¨acklund transformations and Riemann-Hilbert problem for N-wave equations with additional symmetries 12. Georgi Grahovski The Caudrey-Beals-Coifmansystems and the gauge group action 13. Nikolay Kostov The Manakov model as two moving interacting curves 14. Stoil Donev Integrability, curvature and description of photon-like objects April24,2007 17:34 WSPC-ProceedingsTrimSize:9inx6in pcsvf2006 Contributed communications ix 15. Tadashi Sugiyama Characterizationof totally umgilic immersions by curves of order 2 16. Kouei Sekigawa Some critical almost K¨ahler structures 17. Sadahiro Maeda Characterization of parallel isometric immersions of space forms into space forms in the class of isotropic immersions 18. Milen Hristov On the real hypersurfaces of Hermitian manifolds 19. Galya Nakova On some non-integrable almost contact manifolds with Norden metric of dimension 5 20. Bozhidar Iliev Normal frames and linear transports along paths in line bundles. Ap- plications to classical electrodynamics 21. Velichka Milousheva On the geometric structure of hypersurfaces of conullity two in Eu- clidean space 22. Mancho Manev On quasi-Ka¨hler manifolds with Norden metric 23. Dobrinka Gribacheva Lie groups as four-dimensional Riemannian product manifolds 24. Marta Teofilova Lie groups as several complex manifolds with Norden metric 25. Vladimir Balan KCC and linear stability for the Parkinsontremor model 26. Stancho Dimiev Bi-complex analytic pseudo-Euclidean geometry and applications 27. Nikolai Nikolov On the definition of Kobayashi-Busemanpseudometric 28. Petar Stoev Differential forms of bi-complex variables 29. Branimir Kiradjiev Quadratic forms on the bi-complex algebras 30. Lilya Apostolova Real analyticity of the hyper-K¨ahler almost K¨ahler manifolds