Related papers: Efficient computation of null affine parameters
In physics geometrical connections are the mean to create models with local symmetries (gauge connections), as well as general diffeomorphisms invariance (affine connections). Here we study the irreducible tensor decomposition of…
Geodesic models are known as an efficient tool for solving various image segmentation problems. Most of existing approaches only exploit local pointwise image features to track geodesic paths for delineating the objective boundaries.…
Killing vector fields in three dimensions play important role in the construction of the related spacetime geometry. In this work we show that when a three dimensional geometry admits a Killing vector field then the Ricci tensor of the…
We construct new explicit vacuum solutions of quadratic metric-affine gravity. The approach of metric-affine gravity in using an independent affine connection produces a theory with 10+64 unknowns, which implies admitting torsion and…
The goal of this presentation is to build an efficient non-parametric Bayes classifier in the presence of large numbers of predictors. When analyzing such data, parametric models are often too inflexible while non-parametric procedures tend…
An exhaustive list of four-dimensional $\Lambda$-vacuum spacetimes admitting a Killing vector whose self-dual Killing two-form ${\cal F}$ is null is obtained assuming that the self-dual Weyl tensor is proportional to the tensor product of…
For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose…
We study the completeness of light trajectories in certain spherically symmetric regular geometries found in Palatini theories of gravity threaded by non-linear (electromagnetic) fields, which makes their propagation to happen along…
In order to do relativistic gravimetry one needs to define a system of null coordinates for a given constellation of satellites. We present here three methods in order to find the null coordinates of an event in a Schwarzschild geometry. We…
We show how geodesics, Jacobi vector fields and flag curvature of a Finsler metric behave under Zermelo deformation with respect to a Killing vector field. We also show that Zermelo deformation with respect to a Killing vector field of a…
In this paper we consider homothetic Killing vectors in the class of stationary axisymmetric vacuum (SAV) spacetimes, where the components of the vectors are functions of the time and radial coordinates. In this case the component of any…
In an earlier paper (Class. Quantum Grav. 19 (2002) p.259) the author wrote the homothetic equations for vacuum solutions in a first order formalism allowing for arbitrary alignment of the dyad. This paper generalises that method to…
We study the complete conformal geometry of shear-free spacetimes with spherical symmetry and do not specify the form of the matter content. The general conformal Killing symmetry is solved and we can explicitly exhibit the vector. The…
We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The…
We initiate the study of null line defects in Lorentzian conformal field theories in various dimensions. We show that null lines geometrically preserve a larger set of conformal isometries than their timelike and spacelike counterparts,…
Conformal transformations play a widespread role in gravity theories in regard to their cosmological and other implications. In the pure metric theory of gravity, conformal transformations change the frame to a new one wherein one obtains a…
The defining equations for Killing vector fields and conformal Killing vector fields are overdetermined systems of PDE. This makes it difficult to solve the systems numerically. We propose an approach which reduces the computation to the…
Affine geometry is usually regarded as a framework in which metric notions such as distance and angle are absent. However, just as projective geometry produces various metric geometries by introducing additional structures on the line at…
Incomplete data are often represented as vectors with filled missing attributes joined with flag vectors indicating missing components. In this paper we generalize this approach and represent incomplete data as pointed affine subspaces.…
We consider non-expanding shear free (NE-SF) null surface geometries embeddable as extremal Killing horizons to the second order in Einstein vacuum spacetimes. A NE-SF null surface geometry consists of a degenerate metric tensor and a…