It is shown that the projectivised tangent bundle of Finsler spaces with the Chern connection has a contact metric structure under a conformal transformation with certain condition of the Finsler function and moreover it is locally isometric to E × Sm−1(4) for m > 2 and flat for m = 2 if and only if the Cartan tensor vanishes, i.e., the Finsler space is a Riemannian manifold. M.S.C. 2000: 53C60...

Deformation theory requires solving Maurer-Cartan equation (MCE) associated to an DGLA (L-infinity algebra). The universal solution of [HS] is obtained iteratively, as a fixed point of a contraction, analogous to the Picard method. The role of the Kuranishi functor in this construction is emphasized. The parallel with Lie theory suggests that deformation theory is a higher “dimensional” version...

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe θ and a (metric compatible) Lorentz connection Γ . These two potentials yield the field strengths torsion T and curvature R . Evans tried to infuse electromagnetic properties into thi...

We conjecture a geometrical form of the Paley–Wiener theorem for the Dunkl transform and prove three instances thereof, by using a reduction to the one-dimensional even case, shift operators, and a limit transition from Opdam’s results for the graded Hecke algebra, respectively. These Paley– Wiener theorems are used to extend Dunkl’s intertwining operator to arbitrary smooth functions. Furtherm...

The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor connections, the various structures they can preserve, and their geometric interpretations. Preserved subbundles of the Tractor bundle generate foliations with Ricci-f...

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe θ and a (metric compatible) Lorentz connection Γ . These two potentials yield the field strengths torsion T and curvature R . Evans tried to infuse electromagnetic properties into thi...

Since its introduction by Élie Cartan, the holonomy of a connection has played an important role in differential geometry. One of the best known results concerning holonomy is Berger’s classification of the possible holonomies of Levi-Civita connections of Riemannian metrics. Since the appearance of Berger [1955], much work has been done to refine his list of possible Riemannian holonomies. See...

Some general Finsler connections are defined. Emphasis is being made on the Cartan tensor and its derivatives. Vanishing of the hv-curvature tensors of these connections characterizes Landsbergian, Berwaldian as well as Riemannian structures. This view point makes it possible to give a smart representation of connection theory in Finsler geometry and yields to a classification of Finsler connec...

This is a survey on recent joint work with A.R. Gover on the geometry of non–degenerate CR manifolds of hypersurface type. Specifically we discuss the relation between standard tractors on one side and the canonical Cartan connection, the construction of the Fefferman space and the ambient metric construction on the other side. To put these results into perspective, some parts of the general th...