Related papers: Isometries from gauge transformations
Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps…
In this paper we consider the problem of identifying a connection $\nabla$ on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian $\nabla^*\nabla$ over conformally transversally anisotropic…
Ehlers, Pirani, and Schild argued that measurements of null and timelike geodesics yield Weyl and projective connections, respectively, with compatibility in the lightlike limit giving an integrable Weyl connection. Their conclusions hold…
Within the framework of a Kaluza-Klein theory, we provide the geometrization of a generic (Abelian and non-Abelian) gauge coupling, which comes out by choosing a suitable matter fields dependence on the extra-coordinates. We start by the…
We describe the isometry group of $L^2(\Omega, M)$ for Riemannian manifolds $M$ of dimension at least two with irreducible universal cover. We establish a rigidity result for the isometries of these spaces: any isometry arises from an…
In this paper we show that if one writes down the structure equations for the evolution of a curve embedded in an (n)-dimensional Riemannian manifold with constant curvature this leads to a symplectic, a Hamiltonian and an hereditary…
We deal with the problem of identifying a background structure and its perturbation in tetrad theories of gravity. Starting from a peculiar trivial principal bundle we define a metric which depends only on the gauge connection. We find the…
We develop a boundary only method for computing weak gravitational deflection angles at finite source and receiver distances within the Gauss-Bonnet theorem formulation of optical geometry. Exploiting the fact that the relevant equatorial…
It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential…
A vector field on a Riemannian manifold is called conformal Killing if it generates one-parameter group of conformal transformations. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of…
Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…
The Standard Model of particle physics describes electromagnetic, weak, and strong interactions, which are three of the four known fundamental forces of nature. The unification of the fourth interaction, gravity, with the Standard Model has…
Geometric mechanics is a branch of mathematical physics that studies classical mechanics of particles and fields from the point of view of geometry. In a geometric language, symmetries can be expressed in a natural manner as vector fields…
A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold ${\mathcal M}^2$ which can be realized as isometric immersions into $\R^3$. This problem can be formulated as…
A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two…
Contact path geometries are curved geometric structures on a contact manifold comprising smooth families of paths modeled on the family of all isotropic lines in the projectivization of a symplectic vector space. Locally such a structure is…
We study uniqueness of positive solutions to the conformal scalar curvature equation on complete Riemannian manifolds with constant negative scalar curvature. We apply the results to show that conformal transformations on certain complete…
This paper develops a mirror symmetry theory of Spencer cohomology within the geometric framework of constrained systems on principal bundles, revealing deep symmetric structures in constraint geometry. Based on compatible pairs…
Discovery that gravitational field equations may coerce the spacetime metric with isometries to attain a block-diagonal form compatible with these isometries, was one of the gems built into the corpus of black hole uniqueness theorems. We…
We focus on the geometrical reformulation of free higher spin supermultiplets in $4\rm{D},~\mathcal{N}=1$ flat superspace. We find that there is a de Wit-Freedman like hierarchy of superconnections with simple gauge transformations. The…