相关论文: Coordinate Geometric Generalization of the Spherom…

Astrometry is a powerful technique in astrophysics to measure three-dimensional positions of stars and other astrophysical objects, including exoplanets and the gravitational influence they have on each other. Interferometric astrometry is…

A geodesic cycle is a closed curve that connects finitely many points along geodesics. We study geodesic cycles on the sphere in regard to their role in equal-weight quadrature rules and approximation.

In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modelling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely…

This is a survey of metric properties of non-Euclidean conics, mainly based on works of Chasles and Story. A spherical conic is the intersection of the sphere with a quadratic cone; similarly, a hyperbolic conic is the intersection of the…

We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…

Sky coverage is one of the most important pieces of information about astronomical observations. We discuss possible representations, and present algorithms to create and manipulate shapes consisting of generalized spherical polygons with…

We address the issue of angular measure, which is a contested issue for the International System of Units (SI). We provide a mathematically rigorous and axiomatic presentation of angular measure that leads to the traditional way of…

Starting from a general transformation for spherically symmetric metrics where g\_11=-1/g\_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one…

Sphericity and roundness are fundamental measures used for assessing object uniformity in 2D and 3D images. However, using their strict definition makes computation costly. As both 2D and 3D microscopy imaging datasets grow larger, there is…

The concept of boundary plays an important role in several branches of general relativity, e.g., the variational principle for the Einstein equations, the event horizon and the apparent horizon of black holes, the formation of trapped…

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have…

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…

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…

This paper presents necessary, sufficient, and equivalent conditions for the spherical convexity of non-homogeneous quadratic functions. In addition to motivating this study and identifying useful criteria for determining whether such…

A coordinate system is proposed that replaces the usual three-dimensional Cartesian x,y,z position coordinates, for use in robotic localization applications. Range, azimuth, and elevation measurement models become greatly simplified, and,…

A nonrelativistic quantum mechanical particle moving freely on a curved surface feels the effect of the nontrivial geometry of the surface through the kinetic part of the Hamiltonian, which is proportional to the Laplace-Beltrami operator,…

One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…

One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this…

We study collections of curves in generic position on a closed surface whose complement consists of one disk only, up to orientation-preserving homeomorphism of the surface. We define a surgery operation on the set of such collections and…

In this paper we introduce the Constant Width Measure Set, which measures the constant width property of an oval, i.e. the planar simple closed strictly convex curve. We study its geometrical properties. We find the exact relation between…