CONTENTS Preface...........................................................vii List of Participants...............................................ix Part I. RIEMANNIAN GEOMETRY A. Arvanitoyeorgos $SO(n)$--invariant Einstein metrics on Stiefel manifolds............1 C.-L. Bejan 2-codimensional lightlike submanifolds of almost para-Hermitian manifolds...........................................................7 A. Bucki Representation of the Lie group of automorphisms of an almost $r$-paracontact Riemannian manifolds of $P$-Sasakian type..........19 F. Gimenez A lower bound for the radius of the smallest ball containing a manifold with curvature bounded from above.......................29 R. Ivanova On the geometry of some 4-dimensional Einstein manifolds..........35 J. Mike\v{s} On the general trace decomposition problem.........................45 V. Miquel Some applications of the extrinsic distance to immersed and embedded submanifolds.............................................51 M. Podoksenov Lorentzian manifold with a group of conformal transformations that has a normal one-parameter homothety subgroup.................61 N. Pu\v{s}i\'c Some connection class on a hyperbolic Kaehlerian space.............65 M. Rainer, H. J. Schmidt The natural classification of real Lie algebras....................73 E. D. Rodionov Homogeneous Riemannian manifolds with Einstein metrics.............81 V. Rovenskii The integral of mixed scalar curvature along a leaf of foliation..................................................93 S. M. Salamon Orthogonal complex structures.....................................103 H. J. Schmidt On the space of 3-dimensional homogeneous Riemannian manifolds..............................................119 Part II. JETS AND NATURAL OPERATORS A. Cabras The Ricci identity for general connections........................121 A. \v{C}ap A note on endomorphisms of modules over reductive Lie groups and algebras...........................................127 A. Dekr\'et Almost complex structures and connections on $TM$.................133 M. Doupovec, J. Kurek Liftings of tensor fields to the cotangent bundle.................141 I. Kol\'a\v{r} An infinite dimensional motivation in higher order geometry.......151 J. Mu\~{n}oz Masqu\'e, M. E. Rosado Mar\'\i{}a $\operatorname{Diff}M$ does not act transitively on the solutions of an invariant variational problem on $FM$......................161 A. Nijenhuis Connection-free differential geometry.............................171 J. Slov\'ak On the geometry of almost Hermitian symmetric structures..........191 Y. Villarroel On higher order contact manifolds.................................207 G. Virsik Bunch connections.................................................215 Part III. FURTHER GEOMETRIC STRUCTURES M. A. Akivis On four-dimensional conformal structures..........................231 D. Andrica, C. Pintea Some situations when the topological $\varphi$-category is infinite.......................................................239 M. Bjelica Area and length for roulettes via curvature.......................245 N. Bla\v{z}i\'c, N. Bokan Invariance theory and affine differential geometry................249 M. Fecko 'Falling cat' connections constructed from the momentum map..................................................261 V. I. Glizburg The Cartan connection as an invariant of differential system............................................267 M. Jur\'a\v{s} Generalized Laplace invariants and classical integration methods for second order partial differential equations in the plane......................................................275 P. Multarzy\'nski Differential structures for function spaces.......................285 J. Niki\'c $F(3,1)$-structure on the Lagrangian space and invariant subspaces...............................................293 T. Rybicki Commutators of $C^r$--diffeomorphisms acting along leaves.........299 V. V. Shurygin Smooth connections and horizontal distributions on manifolds over local algebras...............................................309 J. Szenthe Symmetries of Lagrangian fields are homotheties in the homogeneous case...........................................321 A. Van\v zurov\'a Projectors of a 3-web.............................................329 P. Witowicz An existence for submanifolds of higher codimensions..............337 R. Wolak Graphs, Ehresmann connections and vanishing cycles................345 Part IV. ANALYSIS ON MANIFOLDS B. Casciaro, M. Francaviglia, V. Tapia On the variational characterization of generalized Jacobi equations..................................................353 M. Craioveanu, M. Puta On the rigid body with two linear controls........................373 I. S. Krasil'shchik A supersymmetry approach to Poisson structures over differential equations...........................................381 M. Marvan Another look on recursion operators...............................393 R. Matsyuk A first order prolongation of the conventional space..............403 G. Munteanu Techniques of higher order osculator bundle in generalized gauge theory.......................................417 J. Pohjanpelto, I. M. Anderson Infinite dimensional Lie algebra cohomology and the cohomology of invariant Euler--Lagrange complexes: A preliminary report...................................427 J. F. Pommaret Einstein equations do not admit a generic potential...............449 M. Puta On an extension of the 3-dimensional Toda lattice.................455 A. Samokhin Discontinuous symmetries of differential equations................463 J. \v{S}tef\'anek A representation of the variational sequence in higher order mechanics...................................................469 D. Tunitsky Contact equivalence of Monge-Amp\`ere equations with transitive symmetries........................................479 R. Vitolo Some aspects of variational sequences in mechanics................487 Part V. GEOMETRIC METHODS IN MATHEMATICAL PHYSICS V. Aldaya, M. Calixto, J. Guerrero Algebraic versus topologic anomalies..............................495 A. L\'opez Almorox, C. Tejero Prieto Infinitesimal symmetries of Hall effect on Riemann surfaces.......503 A. L\'opez Almorox, C. Tejero Prieto BRST cohomology of the Hall effect on the sphere..................513 J. M. Nunes da Costa, C. M. Marle Reduction of bihamiltonian manifolds and recursion operators......523 M. De Le\'on, D. Mart\'\i{}in de Diego Almost product structures in mechanics...........................539 L. Fatibene, M. Ferraris, M. Francaviglia, M. Godina A geometric definition of Lie derivative for spinor fields........549 G. Fischer Quantization induced by geometry..................................559 G. S. Hall Projective symmetry and holonomy..................................567 J. Jany\v{s}ka, M. Modugno Classical particle phase space in general relativity..............573 L. Klapka Poisson manifolds of geodesic arcs................................603 J. Musilov\'a Variational sequence in higher order mechanics....................613 J. Novotn\'y, O. Stol\'\i{}n A generalized approach to the conservation laws problem in general relativity.............................................625 S. Reuter Conformal transformation of equivalence in quantum cosmology......631 W. Sarlet The geometry of mixed first and second-order differential equations with applications to non-holonomic mechanics......................641 P. K. Smrz Differential geometry and elementary particles....................651