Balkan Journal of GEOMETRY and ITS APPLICATIONS ( BJGA ) Volume 1 Year 1996 Number 1 ISSN 1224-2780 Published by BALKAN SOCIETY OF GEOMETERS Geometry Balkan Press Bucharest, ROMANIA BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS Editorial board Promoters and Founders: C. Udri(te (Bucharest) -Editor-in-Chief Gr.Tsagas (Thessaloniki) -Deputy Editor-in-Chief R.Miron (Iassy) - Honorary Editor Members: M. Anastasiei (Iassy), N. Bokan (Beograd), I. (omi( (Novi Sad), M. Craioveanu (Timi(oara), S. Ianu( (Bucharest), R.M. Santilli (Palm Harbour), P. Stavrinos (Athens), L. Tamassy (Debrecen), E. Vassiliou (Athens) Publication Information Manuscripts, books and journal exchanges and correspondence shall be mailed to: Prof. Dr. Constantin Udri¦te, University POLITEHNICA of Bucharest, Department of Mathematics I, Splaiul Independen‘ei 313, 79590 Bucharest, Rom‚nia. Fax: 401-312.53.65 E-mail:udriste@mathem.pub.ro No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means without obtaining the written permission of the publisher. ( 1996 Geometry Balkan Press. Printed in Romania. Sponsored by: POLITEHNICA UNIVERSITY OF BUCHAREST SOROS FOUNDATION FOR AN OPEN SOCIETY ROMANIA Aims and Scope The Balkan Society of Geometers is an international nonprofit organization. The rule of the Society and application form will be sent to any person on request. BJGA is an international biannual journal. BJGA covers a wide spectrum of pure and applied mathematics, ranging from the synthetic geometry to the computational geometry and applications in physics, chemistry, biology, engineering and architecture promoting especially papers presented at Balkan meetings. The Editorial Board takes a very active role in selecting and refereeing papers, ensuring the best quality of contemporany geometry and its applications. Will be abstracted in: Mathematical Reviews, Zentralblatt f(r Mathematik. Instructions to Authors Two copies of the manuscript in fluent English must be submitted, each complete with all illustrations, together with one set of high-quality line drawings and/or photographs, prepared strictly with a current number of BJGA as a model in matter of form. Submission is a representation that the manuscript has not been published previously nor currently submitted for publication elsewhere. All submissions are assesses by two independent referees. On the first page of the manuscript, the author should provide the title, name, abstract, subject classification, and key words. The affiliation, and complete address (including e-mail or fax) will be written at the end of the paper. Upon acceptance of an article, the authors, will be requested to supply a final copy prepared in Latex, on 3,5" DOS diskettes or via E-mail. If electronic copy is supplied, publication will be accelerated. BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS ______________________________________________________________ Volume 1, Year 1996, Number 1 Contents ii Preface iii The Statute of the Balkan Society of Geometers (BSG) ix Report of the Conference of Founding of BSG x Report on the Meeting of Founders of BSG xii Ruling of Court xiv Application Form xv Memorandum 1 Mihai Anastasiei, Finsler Connections in Generalized Lagrange Spaces 11 Gheorghe Atanasiu, The Equations of Structure of an N-Linear Connection in the Bundle of Accelerations 21 Irena (omi(, The Curvature Theory of Generalized Connection in 31 Radu Iord(nescu, The Geometrical Barbilian's Work from a Modern Point of View 37 Radu Miron, On the Geometries of Superior Order 47 Liviu Nicolescu, Champs des vecteurs remarquables dans l'algebre de deformation: retrospective et perspective 61 Ruggero Maria Santilli, Representation of NonHamiltonian Vector Fields in the Coordinates of the Observer via the Isosymplectic Geometry 75 P.C.Stavrinos, Bianchi Identities, Yang-Mills and Higgs Field Produced on - Deformed Bundle 83 Lajos Tamassy, Metrizability of Affine Connections 91 Grigorios Tsagas, On the Killing Tensor Fields on a Compact Riemannian Manifold 99 Constantin Udri(te, Riemannian Convexity in Programming II 111 Constantin Udri(te, Riemannian Convexity 117 Efstathios Vassiliou, Transformations of Sheaf Connections PREFACE Balkan Society of Geometers (BSG) has been established in order to create better relationships between geometers from Balkan Countries and to improve the research in Geometry and Its Applications all over the World. For this reason the BSG will publish the review Balkan Journal of Geometry and Its Applications (BJGA), reports, books and monographs, by its own publishing house Geometry Balkan Press. Up to now the Society has been officially registered in Romania, having branches in Romania, Greece, Bulgaria, Yugoslavia. In the near future we will try to organize branches in Albania and Turkey. The leaders of BSG (President, Acad.Prof. Dr. Radu Miron; Vice-President Prof. Dr. Grigorios Tsagas; Vice-President Prof. Dr. Constantin Udri(te) gathering on 15-th December 1995 at the Aristotle University of Thessaloniki discussed some problems about the life of the Society and decided the structure of the Editorial Board of the BJGA. Also they decided the first issue of BJGA to contain the Founding Documents of BSG (Statute, Reports, Ruling of Court, Application form, Memorandum) and Papers of some founders. BJGA wellcomes all theoretical and computational advances in geometry and its applications. The contributions will be original research papers proving the relevance of geometry and should be prepared in accordance with the Instructions to Authors. August 30, 1996 Editor-in-Chief ii BJGA VOLUME 1, Number 1, P. i-xv, 1-133, 1996 .