Related papers: Coordinate Geometric Approach to Spherometer
Geometry of the spacetime with a spherical shell embedded in it is studied in two coordinate systems - in Kodama-Schwarzschild coordinates and in Gaussian normal coordinates. We consider transformations between the coordinate systems as in…
The geodesics in various spherical Rindler frames are investigated. A display of some kinematical quantities of the spacetime is given. The constant acceleration from the metric acts as the surface gravity of the horizon $r = 0$. The radial…
Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…
Astrometry measures shifts in a star's photocentre and can be used to detect reflex motion due to orbiting exoplanets. Brightness asymmetries (e.g. starspots) rotating in and out of view can also cause apparent motion of the photocenter,…
In the paper, some geometric properties of the plane interception curve defined by a nonlinear ordinary differential equation are discussed. Its parametric representation is used to find the limits of some triangle elements associated with…
We embark in a program of studying the problem of better approximating surfaces by triangulations(triangular meshes) by considering the approximating triangulations as finite metric spaces and the target smooth surface as their…
The problem of defining correctly geometric objects such as the curvature is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs.…
Inspired by a formula of Stern that relates scalar curvature to harmonic functions, we evaluate the mass of an asymptotically flat $3$-manifold along faces and edges of a large coordinate cube. In terms of the mean curvature and dihedral…
The discrete ordinates method with angular parameters is discussed in light of the recent extension of its underlying hypothesis. The analysis shows that the method, although it compares very well with the trajectory of photons model, it…
In this paper we consider a semitetrad covariant decomposition of spherically symmetric spacetimes and find a governing hyperbolic equation of the Gaussian curvature of two dimensional spherical shells, that emerges due to the…
It is common in Physiological Optics to fit the corneal and the lens surfaces to conic-based surfaces (usually ellipse-based surfaces), obtaining their characteristic radius of curvature and asphericity. Here we show that the variation in…
In Finsler geometry, we use calculus to study the geometry of regular inner metric spaces. In this note I will briefly discuss various curvatures and their geometric meanings from the metric geometry point of view, without going into the…
In this short note, we compute the conformal stereographic projection on the standard metric of a sphere quotient. The result is a Majumdar-Papapetrou metric, which might be useful.
In the current paper, first we give the correct version of the formula for mean Berwald curvature of a spherically symmetric Finsler metric given in paper \cite{YCheWSon2015}. Further, we establish differential equations characterizing…
See http://www.youtube.com/watch?v=izbGXdjvK_I for a YouTube video showing part of the results in this paper.We will consider surfaces whose mean curvature at a point is a linear function of the square of the distance from that point to the…
In this paper, we define a new type of ruled surface called ruled surface by using the alternative frame of a base curve. Then, we study its differential geometric properties such as striction line, distribution parameter, fundamental…
Circular and radial geodesics are studied in the spacetime described by the $\gamma$ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical…
The turnaround radius of a large structure in an accelerating universe has been studied only for spherical structures, while real astronomical systems deviate from spherical symmetry. We show that, for small deviations from spherical…
The Peirce quincuncial projection is a mapping of the surface of a sphere to the interior of a square. It is a conformal map except for four points on the equator. These points of non-conformality cause significant artifacts in photographic…
We are interested in the development of spherically symmetric geometries in $F(T)$ teleparallel gravity which are of physical importance. We first express the general forms for the spherically symmetric frame and the zero curvature, metric…