On simultaneous integrability of two commuting almost tangent structures
On the algebraic hull of an automorphism group of a principal bundle.
On the automorphism group of a compact Lorentz manifold and other geometric.
On the characteristic connection of gwistor space
We give a brief presentation of gwistor spaces, which is a new concept from G 2 geometry. Then we compute the characteristic torsion T c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T c is ∇c-parallel; this allows for the classification of the G 2 structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged.
On the geometry of frame bundles
Let be a Riemannian manifold, its frame bundle. We construct new examples of Riemannian metrics, which are obtained from Riemannian metrics on the tangent bundle . We compute the Levi–Civita connection and curvatures of these metrics.
On the Lie algebra of vertical prolongation operators
On the structure function of a -structure
On totally umbilical cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of Cayley algebra
On transverse structures of foliations
On weakly symmetric and special weakly Ricci symmetric Lorentzian -Kenmotsu manifolds.
Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles
Let be a principal bundle of frames with the structure group . It is shown that the variational problem, defined by -invariant Lagrangian on , can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.
Penrose's tensors. II.
Penrose's tensors on supergrassmannians.
...-platitude des Structures de Contact.
Projectively Anosov flows with differentiable (un)stable foliations
We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on which can be extended on a neighbourhood of into a projectively Anosov flow so that is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on . In this case, the only flows on which extend to ...
Quaternionic-like structures on a manifold: Note I. 1-integrability and integrability conditions
This Note will be followed by a Note II in these Rendiconti and successively by a wider and more detailed memoir to appear next. Here six quaternionic-like structures on a manifold (almost quaternionic, hypercomplex, unimodular quaternionic, unimodular hypercomplex, Hermitian quaternionic, Hermitian hypercomplex) are defined and interrelations between them are studied in the framework of general theory of G-structures. Special connections are associated to these structures. 1-integrability and...
Quaternionic-like structures on a manifold: Note II. Automorphism groups and their interrelations
We consider different types of quaternionic-like structures. The interrelations between automorphism groups of the subordinated structures and of some admissible connections are studied. A characterization of automorphisms of a quaternionic structure as some kind of projective transformations is given. General results on harmonicity of an automorphism of some -structure are obtained and applied to the case of an almost Hermitian quaternionic structure. Different noteworthy transformations groups...
Quelques propriétés des -structures
Recent advances in the theory of holonomy
Reduction of Complex Hamiltonian G-Spaces.