Asymptotic behaviour of SU (2) monopole metric.
Canonical nonlinear connections in the multi-time Hamilton geometry.
Circle-valued Morse theory and Reidemeister torsion.
Classes caractéristiques secondaires des fibrés plats
Clifford-Kähler manifolds.
Compact 3-manifolds with a flat Carnot-Carathéodory metric
Connections on embedded manifolds.
Connections with prescribed curvature and Yang-Mills currents : the semi-simple case
Corrections to "L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper triangular matrices" (Fund. Math. 156 (1998), 99–110)
Curvatures of the diagonal lift from an affine manifold to the linear frame bundle
We investigate the curvature of the so-called diagonal lift from an affine manifold to the linear frame bundle LM. This is an affine analogue (but not a direct generalization) of the Sasaki-Mok metric on LM investigated by L.A. Cordero and M. de León in 1986. The Sasaki-Mok metric is constructed over a Riemannian manifold as base manifold. We receive analogous and, surprisingly, even stronger results in our affine setting.
Derivational equations of submanifolds in an asymmetric affine connection space
Differential and geometric structure for the tangent bundle of a projective limit manifold
Differential geometric structures of stable state feedback systems with dual connections
Distinguished connections on -metric manifolds
We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of -metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among connections. We prove that the first canonical and the well adapted connections define a one-parameter family of adapted...
Distinguished Riemann-Hamilton geometry in the polymomentum electrodynamics
In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics.
Do Barbero-Immirzi connections exist in different dimensions and signatures?
We shall show that no reductive splitting of the spin group exists in dimension other than in dimension . In dimension there are reductive splittings in any signature. Euclidean and Lorentzian signatures are reviewed in particular and signature is investigated explicitly in detail. Reductive splittings allow to define a global -connection over spacetime which encodes in an weird way the holonomy of the standard spin connection. The standard Barbero-Immirzi (BI) connection used in LQG is...
Einstein equations for -Berwald-Moor relativistic models.
Einstein metrics and stability for flat connections on compact Hermitian manifolds, and a correspondence with Higgs operators in the surface case.
Einstein-Yang Mills equations for gauge transformations of second order.
Ellipticity of the symplectic twistor complex
For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain infinite rank vector bundles defined over this manifold. The differential operators are symplectic analogues of the twistor operators known from Riemannian or Lorentzian spin geometry. It is known that the mentioned sequences form complexes if the symplectic...