相关论文: Five-Dimensional Tangent Vectors in Space-Time

General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…

The quest for a consistent theory for quantum gravity is one of the most challenging problems in theoretical high-energy physics. An often-used approach is to describe the gravitational degrees of freedom by the metric tensor or related…

The invariant projections of the energy-momentum tensors of Lagrangian densities for tensor fields over differentiable manifolds with contravariant and covariant affine connections and metrics [$(\bar{L}_n,g)$-spaces] are found by the use…

In models of the Universe with extra dimensions gravity propagates in the whole space-time. Graviton production by matter on the brane is significant in the early hot Universe. In a model of 3-brane with matter embedded in 5D space-time…

Defining the electric and magnetic field vectors in curved spacetime requires a proper choice of the observer's frame four-vector. Related literature shows that this fundamental issue in physics still needs to be properly resolved. In…

In this talk notes we expose the possibility to induce the cosmological constant from extra dimensions, in a geometrical framework where our four-dimensional Riemannian space-time is embedded into a five-dimensional Weyl integrable space.…

There exist at least a few different kind of averaging of the differences of the energy-momentum and angular momentum in normal coordinates {\bf NC(P)} which give tensorial quantities. The obtained averaged quantities are equivalent…

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…

The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the Schouten-Nijenhuis…

The linear transports along paths in vector bundles introduced in Ref. [1] are applied to the special case of tensor bundles over a given differentiable manifold. Links with the transports along paths generated by derivations of tensor…

Connections are an important tool of differential geometry. This paper investigates their definition and structure in the abstract setting of tangent categories. At this level of abstraction we derive several classically important results…

We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichm\"uller Space: (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The…

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…

The paper considers the formulation of higher-order continuum mechanics on differentiable manifolds devoid of any metric or parallelism structure. For generalized velocities modeled as sections of some vector bundle, a variational kth order…

An expression is derived where the mass is connected to an integral over the pressure of gravitating matter in the frame work of five dimensional(5D) space-time.

Higher-rank Minkowski valuations are efficient means for describing the geometry and connectivity of spatial patterns. We show how to extend the framework of the scalar Minkowski valuations to vector- and tensor-valued measures. The…

The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations…

Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…

This is a brief review of the superspace formulation for five-dimensional N=1 matter-coupled supergravity recently developed by the authors.

The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables…