This article is motivated by the theory of distinguished curves in parabolic geometries, as developed in [2]. A parabolic geometry is, by definition, modelled on a homogeneous space of the form G/P where G is a real semisimple Lie group and P is a parabolic subgroup. (There is also a complex theory which corresponds to the choices of complex G’s and P ’s with specific curvature restrictions for...

The classical Cartan’s structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. In order to study the mathematical properties of singularities, we need to study the geometry of manifolds endowed on the tangent bundle with a symmetric bilinear form which is allowed to become degenerate. B...

In this paper, we study the theory of geodesics with respect to the TanakaWebster connection in a pseudo-Hermitian manifold, aiming to generalize some comparison results in Riemannian geometry to the case of pseudo-Hermitian geometry. Some HopfRinow type, Cartan-Hadamard type and Bonnet-Myers type results are established.

The current paper is devoted to the study of integral curves of constant type in parabolic homogeneous spaces. We construct a canonical moving frame bundle for such curves and give the criterium when it turns out to be a Cartan connection. Generalizations to parametrized curves, to higher-dimensional submanifolds and to general parabolic geometries are discussed.

The geometry of an admissible Bäcklund transformation for an exterior differential system is described by an admissible Cartan connection for a geometric structure on a tower with infinite–dimensional skeleton which is the universal prolongation of a |1|–graded semi-simple Lie algebra. 2000 MSC: 14M17,53C05,53C10,53C30, 58J70,58J72,58A15.

We derive and discus the equations of motion for spinless matter: relativistic spinless scalar fields, particles and fluids in the recently proposed by A. Saa model of gravity with covariantly constant volume with respect to the transposed connection in Einstein-Cartan spaces. A new interpretation of this theory as a theory with variable Plank ”constant” is suggested.

Inflation in the framework of Einstein-Cartan theory is revisited. a natural extension General Relativity, with non-vanishing torsion. The connection on Riemann-Cartan spacetime only compatible cosmological principal for particular form We show this to also be gauge invariance principle non-Abelian and Abelian fields under certain deviced minimal coupling procedure. adopt an field "cosmic triad...

We classify compact manifolds of dimension three equipped with a path structure and fixed contact form (which we refer to as strict structure) under the hypothesis that their automorphism group is non-compact. use Cartan connection associated show its curvature constant.

New examples of the theory recently proposed by Ricca [PRA(1991)] on the generalization of Da RiosBetchov intrinsic equations on curvature and torsion of classical non-Riemannian vortex higher-dimensional string are given. In particular we consider applications to 3-dimesional fluid dynamics, including the case of a twisted flux tube and the fluid rotation. In this case use is made of Da Rios e...

The aim of the present paper is to provide an intrinsic investigation of the fundamental properties of the most important geometric objects associated with the fundamental linear connections on a Finsler manifold. We introduce and investigate intrinsically the most general properties concerning the torsion tensor fields and the curvature tensor fields associated with a certain regular connectio...