相关论文: Five-Dimensional Tangent Vectors in Space-Time
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
Futher development is made of a consept of space-time as multidimensional elastic plate, proposed earlier in [20,21]. General equilibrium equations, including 4-dimensional tangent stress tensor - energy-momentum tensor of matter - are…
Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract…
Torsion appears in literature in quite different forms. Generally, spin is considered to be the source of torsion, but there are several other possibilities in which torsion emerges in different contexts. In some cases a phenomenological…
We investigate a tangent space at a point of a general metric space and metric space valued derivatives. The conditions under which two different subspace of a metric space have isometric tangent spaces in a common point of these subspaces…
For each relative $\operatorname{GL}(V)$-invariant tensor $I\in \Lambda^{p_1+1}V^{\vee}\otimes .. \otimes \Lambda^{p_n+1}V^{\vee}$ we construct a $\operatorname{GL}(V)$-invariant weighted differential form $\eta$ on $(\mathbb{P} V)^{n}$.…
A new object, called the velocity tensor, is introduced. It allows to formulate a generally covariant mechanics. Some properties of the velocity tensor are derived.
Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to…
Recently, it was shown that the quantum effects of the matter, could be used to determine the conformal degree of freedom of the space-time metric. So both gravity and quantum are geometrical features. Gravity determines the causal…
A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their…
In this contribution I intend to give a summary of the new relevant results obtained by using the general superenergy tensors. After a quick review of the definition and properties of these tensors, several of their mathematical and…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
Since the early days of the theory of electromagnetism and of gravity the idea of space, then space-time, as a sort of physical continuum hovered the scientific community. Actually general relativity shows the strong similarity that exists…
A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of…
In present work the generalization of Einstein's special theory of relativity on 5-dimentional space is considered, in which as fifth coordinates we consider the interval s of a particle. 5-dimentional vectors in this space are isotropic…
The properties of 5D gravitational flux tubes are considered. With the cross section and 5th dimension in the Planck region such tubes can be considered as string-like objects, namely $\Delta-$strings. A model of attachment of…
There are a number of algebraic classifications of spacetimes in higher dimensions utilizing alignment theory, bivectors and discriminants. Previous work gave a set of necessary conditions in terms of discriminants for a spacetime to be of…
A purely algebraic construction of super-energy tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an…
For more than half a century, moments have attracted lot ot interest in the pattern recognition community.The moments of a distribution (an object) provide several of its characteristics as center of gravity, orientation, disparity, volume.…
This article is a description of elasticity theory for readers with mathematical background. The first sections are an abridgment of parts of the book by Marsden and Hughes, including a compact identification of the equations of motion as…