New Developments in Differential Geometry

In succession to our former meetings on differential geometry a Colloquium took place in Debrecen from July 26 to July 30, 1994. The Colloquium was organized by the University of Debrecen, the Debrecen Branch of the Hungarian Academy of Sciences and supported by the Janos Bolyai Mathematical Society. The Colloquium and especially this proceedings volume received an important financial contribution form OMFB in the framework of the ACCORD Programme no. H9112-0855. The Organizing Committee was the following: S. Bacso, P.T. Nagy, L. Kozma (secretary), Gy. Soos, J. Szenthe (chairman) and L. Tamassy (chairman). It was pleasant to meet both the returning participants of our former colloquia and the numerous new guests. The Colloquium had 68 participants from 22 foreign countries and 18 from Hungary. At the opening we commemorated the 25th anniversary of the death of Otto Varga, the late Professor of the Debrecen University, one of the founders of Finsler geometry, the master of many differential of our country. The programme included 10 plenary lectures from: P.B. geometers Gilkey, R. Miron, I. Kolar, B. Wegner, D. Lehmann, o. Kowalski, T. Otsuki, K.B. Marathe, M. Crampin, W. Sarlet and 68 short lectures in 3 sections. The meeting created an inspiring atmosphere for fruitful discussions between the participants. The historical sites of the town Debrecen and its famous surroundings offered ideal to get to know Hungarian cultural traditions and for evening programmes.

Proceedings of the Colloquium on Differential Geometry, Debrecen, Hungary, July 26-30, 1994

Inhalt
Preface. List of participants. Hypercomplex structures on quaternionic manifolds; D.V. Alekseevsky, S. Marchiafava. Time inversion in physics; T. Antal. Non commutative geometry of GLp-Bundles; A. Asada. Totally umbilical degenerate Monge hypersurfaces of R42; A. Bejancu. The left exactness of the smooth left Puppe sequence; P. Cherenack. A linear connection associated with any second order differential equation field; M. Crampin. Geometry of geodesic tubes on Sasakian manifolds; M. Djoric. Classification of differential (n-1)-forms on an n-dimensional manifold with boundary; W. Domitrz. Natural relations between connections in 2-fibred manifolds; M. Doupovec, A. Vondra. Connections on higher order frame bundles; M. Elzanowski, S. Prishepionok. The differential geometry of Cosserat media; M. Epstein, M. de León. The parametric-manifold approach to canonical gravity; G. Fodor, Z. Perjés. Admissible operations and product preserving functors; J. Gancarzewicz, et al. Curvature properties of para Kähler manifolds; E. García-Río, et al. Four dimensional Osserman Lorentzian manifolds; E. García-Río, D.N. Kupeli. The eta invariant and the equivariant spin bordism of spherical space form 2 groups; P.B. Gilkey, B. Botvinnik. On locally conformal Kähler structures; T. Kashiwada. Torsion-free connections on higher order frame bundles; I. Kolár. The trace decomposition of tensors of type (1,2) and (1,3); D. Krupka. Higher-order constrained systems on fibred manifolds: An exterior differential systems approach; O. Krupková. The method of separation of variables for Laplace-Beltrami equation in semi-Riemannian geometry; D.N.Kupeli. A geometrical approach to classical field theories: a constraint algorithm for singular theories; M. de León, et al. Noether type theorems in higher order analytical mechanics; R. Miron. The electromagnetic field in the higher order relativistic geometrical optics; R. Miron, T. Kawaguchi. On a Riemannian approach to the order &agr; relative entropy; M. Miyata, et al. A differential equation related with some general connections; T. Otsuki. On quasi connections on fibred manifolds; P. Popescu. Diffeomorphism groups of a manifold with boundary; T. Rybicki. Separability of time-dependent second-order equations; W. Sarlet. The field equations of generalized conformally flat spaces of metric g&mgr;&ngr; (x, &xgr; &xgr;¯ = e2&sgr;(x,&xgr;,&xgr;¯) &eegr;&mgr;&ngr;; P.C. Stavrinos, et al. Symmetries of sprays and admissible Lagrangians; J. Szenthe. Curvature of submanifolds in points Finsler spaces; L. Tamássy. Special vector fields on a compact Riemannian manifold; G. Tsagas. Magnetic dynamical systems; C. Udrişte, et al. Totally geodesic orbits in homogeneous spaces; Y. Villarroel. Parallel and transnormal curves on surfaces; B. Wegner.