A new set of canonical variables for the Hamiltonian treatment of general relativity was introduced by Ashtekar [1]. The new set of canonical variables are the triads E i (the projections of the tetrads onto a three-surface) and a complex SU(2) connection Aax. The introduction has opened new possibilities of achieving a Dirac canonical quantization of the gravitational field. It was shown that ...

We study the dynamic and thermodynamic origin of non-canonical equilibria, and we discuss their connection with the generalized central limit theorem and the micro-canonical Boltzmann principle. We reach the conclusion that the zeroth law of thermodynamics and the Boltzmann principle are fulfilled thanks to an apparent fault turned into a benefit: the dynamic approach can only produce a truncat...

We give a simple interpretation of the adapted complex structure of Lempert-Szőke and Guillemin-Stenzel: it is given by a polar decomposition of the complexified manifold. We then give a twistorial construction of an SO(3)-invariant hypercomplex structure on a neighbourhood of X in TTX, where X is a real-analytic manifold equipped with a linear connection. We show that the Nahm equations arise ...

The structure algorithm provides an extension to nonlinear systems of the Kronecker canonical forms relative to linear constant-coefficient implicit differential systems. A connection with the index problem is sketched in the conclusion.

We give canonical resolutions of singularities of several cone varieties arising from invariant theory. We establish a connection between our resolutions and resolutions of singularities of closure of conjugacy classes in classical Lie algebras.

The moduli space of jets of certain G-structures (basically those which admit a canonical linear connection) is shown to be isomorphic to the quotient of a natural G-module by G.

Adopting the pullback approach to Finsler geometry, the aim of the present paper is to provide intrinsic (coordinate-free) proofs of the existence and uniqueness theorems for the Chern (Rund) and Hashiguchi connections on a Finsler manifold. To accomplish this, we introduce and investigate the notions of semispray and nonlinear connection associated with a given regular connection, in the pullb...

We describe recent attempts at discretizing canonical quantum gravity in four dimensions in terms of a connection formulation. This includes a general introduction, a comparison between the real and complex connection approach, and a discussion of some open problems. (Contribution to the proceedings of the workshop “Recent mathematical developments in classical and quantum gravity”, Sintra, Por...

The research was carried out in order to determine the infl uence of morphological characteristics, motor and functional abilities (predictor sets) on the athletics program content of physical education (criterion set) of the elementary school students. A sample of 105 respondents was taken from the population of the seventh and eighth grade male students of elementary schools in Nis. 14 measur...