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