Related papers: A Historical Perspective on the Topology and Physi…

It is a brief review of the physical theories embodying the idea of extra dimensions, starting from the pre-historic times to the present day. Here we have classified the developments into three eras, such as Pre-Einstein, Einstein and…

Efforts have been made recently to reformulate traditional Kaluza-Klein theory by using a generalized definition of a higher-dimensional extended space-time. Both electromagnetism and gravity have been studied in this context. We review…

We give a brief review of recent developments in five-dimensional theories of spacetime and highlight their geometrical structure mainly in connection with the Campbell-Magaard theorem.

We describe how a physical theory incorporating the properties of fields deriving from extra-dimensional structures over a four-dimensional spacetime manifold can in principle be obtained through the analysis of a simple initial structure…

The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More specifically, our aim is to consider, without a claim to…

During the last century, two independent theories using the concept of dimensional reduction have been developed independently. The first, known as F\"oppl-von K\`arm\`an theory, uses Riemannian geometry and continuum mechanics to study the…

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data…

It took two millennia after Euclid and until in the early 1880s, when we went beyond the ancient axiom of parallels, and inaugurated geometries of curved spaces. In less than one more century, General Relativity followed. At present,…

An elementary survey of mathematical cosmology is presented. We cover certain key ideas and developments in a qualitative way, from the time of the Einstein static universe in 1917 until today. We divide our presentation into four main…

The formal structure of the early Einstein's Special Relativity follows the axiomatic deductive method of Euclidean geometry. In this paper we show the deep-rooted relation between Euclidean and space-time geometries that are both linked to…

This is an expository treatise on the development of the classical geometries, starting from the origins of Euclidean geometry a few centuries BC up to around 1870. At this time classical differential geometry came to an end, and the…

In this brief review we discuss the viability of a multidimensional geometrical theory with one compactified dimension. We discuss the case of a Kaluza Klein fifth dimensional theory, addressing the problem by an overview of the…

I address the issue of spacetime dimensionality within Kaluza-Klein theories and theories with large extra dimensions. I review the arguments explaining the dimensionality of the universe, within the framework of string gas cosmology and…

The Kaluza-Klein idea of extra spacetime dimensions continues to pervade current attempts to unify the fundamental forces, but in ways somewhat different from that originally envisaged. We present a modern perspective on the role of…

We examine the challenge of viewing all the fields in supergravity as arising from a Kaluza-Klein like dimensional reduction of some higher-dimensional theory. This gives rise to what is known as exceptional field theory or double field…

We propose in this paper a new approach to the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering a natural geometric definition of 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…

The connection dynamics of the 5-dimensional Kaluza-Klein theory reduced on 4-dimensional spacetime is obtained by performing the Hamiltonian analysis and canonical transformations. Deparametrization is achieved in the spherically symmetric…

After mathematicians and physicists had learned that the structure of physical space was not necessarily Euclidean, it became conceivable that the global topological structure of space was non-trivial. In the context of the late 19th…

In this article, the evolution of the ideas about the fourth spatial dimension is presented, starting from those which come out within classical Euclidean geometry and going through those arose in the framework of non-Euclidean geometries,…