相关论文: Coordinate-free classic geometries

In this article we first develop novel Rindler-type representations of flat spacetime by demonstrating that the standard hyperbolic transformation is a member of an infinite family of coordinate mappings. We specifically introduce cyclic…

Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate…

An effective Lagrangian approach, partly inspired by Quantum Loop Cosmology (QLC), is presented and formulated in a non flat FLRW space-times, making use of modified gravitational models. The models considered are non generic, and their…

In this paper we analyze the normal forms of a general quadratic Hamiltonian system defined on the dual of the Lie algebra $\mathfrak{o}(K)$ of real $K$ - skew - symmetric matrices, where $K$ is an arbitrary $3\times 3$ real symmetric…

This thesis presents a framework in which to explore kinematical symmetries beyond the standard Lorentzian case. This framework consists of an algebraic classification, a geometric classification, and a derivation of the geometric…

In this paper, we try to generalize to the case of compact Riemannian orbifolds $Q$ some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds $M$. We shall also consider the problem of…

Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since…

DeTurck and Yang have shown that in the neighbourhood of every point of a $3$-dimensional Riemannian manifold, there exists a system of orthogonal coordinates (that is, whith respect to which the metric has diagonal form). We show that this…

Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…

We investigate geometric properties of indecomposable but non-irreducible Lorentzian manifolds, which are total spaces of circle bundles. We investigate under which conditions these manifolds are complete and give examples which fulfill the…

In this work, we obtain isotropic extensions of the usual spherically symmetric vacuum geometries in general relativity. Exact and perturbative solutions are derived. The classes of geometries obtained include black holes in compact and…

We considered the most general form of non-static cylindrically symmetric space-times for studying proper curvature symmetry by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature symmetry…

An important problem in quaternionic hyperbolic geometry is to classify ordered $m$-tuples of pairwise distinct points in the closure of quaternionic hyperbolic n-space, $\overline{{\bf H}_\bh^n}$, up to congruence in the holomorphic…

We present some properties of hyperkahler torsion (or heterotic) geometry in four dimensions that make it even more tractable than its hyperkahler counterpart. We show that in $d=4$ hypercomplex structures and weak torsion hyperkahler…

Harmonic maps from Riemann surfaces arise from a conformally invariant variational problem. Therefore, on one hand, they are intimately connected with moduli spaces of Riemann surfaces, and on the other hand, because the conformal group is…

In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable…

Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a…

The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…

This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…

We show how to exploit symmetry assumptions to determine the dynamical equations for the particular geometry that underpins given matter field equations. The procedure builds on the gravitational closure equations for matter models without…