646 Results Found

In shape analysis, the interpolation of shapes’ trajectories is often performed by means of geodesics in an appropriate Riemannian Shape Space. Over the past several decades, different metrics and shape spaces have been proposed, including Kend...

We give a short survey on plurisubharmonic interpolation, with a focus on the possibility of connecting two given plurisubharmonic functions by plurisubharmonic geodesics.

The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodes...

A translation curve in a Thurston space is a curve such that for given unit vector at the origin, the translation of this vector is tangent to the curve in every point of the curve. In most Thurston spaces, translation curves coincide with geodesic l...

A translation curve in a homogeneous space is a curve such that for a given unit vector at the origin, translation of this vector is tangent to the curve in its every point. Translation curves coincide with geodesics in most Thurston spaces, but not...

This paper gives a study of a two dimensional version of the theory of normal surfaces; namely, a study o normal curves and their relations with respect to geodesic curves. This study results with a nice discrete approximation of geodesics embedded i...

The classical uncertainty principle inequalities are imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle is reformulated in terms of proper space–time length element, Planck lengt...

We study the existence and stability of circular geodesics in a family of asymptotically AdS static black holes in New Massive Gravity theory. We show that the mathematical sign of the hair parameter determines the existence of such geodesics. For a...

Recently, the current authors have formulated and extensively explored a rather novel Painlevé–Gullstrand variant of the slow-rotation Lense–Thirring spacetime, a variant which has particularly elegant features—including unit...

This paper introduces an alternative generalization of the static solution with quadrupole moment, the $\mathrm{q}$-metric, that describes a deformed compact object in the presence of the external fields characterized by multipole moments. In addition, we also...

Information geometric optimization (IGO) is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices: the initial problem is transformed into the optimization of a smooth function...

Mobi spaces were introduced by the authors as a possible algebraic axiomatization of spaces in which any two points are connected by a geodesic path. Previous work has focused primarily on the algebraic properties of these structures; here, we return...

We consider the problem of finding the closest multivariate Gaussian distribution on a constraint surface of all Gaussian distributions to a given distribution. Previous research regarding geodesics on the multivariate Gaussian manifold has focused o...

In the context of CAD, CAM, CAE, and reverse engineering, the problem of mesh parameterization is a central process. Mesh parameterization implies the computation of a bijective map $\varphi$ from the original mesh $M\in {\mathbb{R}}^3$ to the planar...

In this paper, we study some homogeneity properties of a semi-direct extension of the Heisenberg group, known in literature as the hyperbolic oscillator (or Boidol) group, equipped with the left-invariant metrics corresponding to the ones of the osci...

In recent years, the modification of general relativity (GR) through $f\left(R\right)$ gravity is widely used to study gravity in a variety of scenarios. In this article, we study various physical properties of a black hole (BH) that emerged in the linear Maxwell...

In this work, we consider holomorphically projective mappings of (pseudo-) Kähler spaces. We determine the conditions for finite complete geodesics that must be satisfied for the mappings to be trivial; i.e., these spaces are rigid.

In the paper, we consider holomorphically projective mappings of n-dimensional pseudo-Riemannian Kähler and hyperbolic Kähler spaces. We refined the fundamental linear equations of the above problems for metrics of differentiability class $C^{}$...

This paper investigates the global dynamics of timelike geodesics of a spherically symmetric black hole under Lorentz-violating effects governed by parameters $\lambda$ (scaling exponent) and ${\rm Y}$ (Lorentz violation strength). By employing dynami...

We investigate null geodesics, photon spheres and black hole shadows for the static spherically symmetric non-Schwarzschild black hole solution of Einstein–Weyl gravity, a higher-derivative extension of General Relativity containing a quadratic...

In the present paper, we study conformal mappings between a connected n-dimension pseudo-Riemannian Einstein manifolds. Let g be a pseudo-Riemannian Einstein metric of indefinite signature on a connected n-dimensional manifold M. Further assume that...

A class of exact (non-perturbative) models of strong gravitational waves based on Shapovalov type III spacetimes and Einstein’s vacuum equations is obtained. Exact solutions are found for the trajectories of particles and radiation in a gravita...

Geodesics (by definition) have an intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration ${\mathrm{d}}^2{x}^i/\mathrm{d}{t}^2$ can very easily be non-zero, and the coordinate velocity $\mathrm{d}{x}^i/\mathrm{d}t$ c...

As a generalization of a geodesic function, this paper introduces the notion of the geodesic ${\phi }_E$-convex function. Some properties of the ${\phi }_E$-convex function and geodesic ${\phi }_E$-convex function are established. The concepts of a geodesic ${\phi }_E$-...

Curves on a polygonal mesh are quite useful for geometric modeling and processing such as mesh-cutting and segmentation. In this paper, an effective method for constructing $C^1$ piecewise cubic curves on a triangular mesh $\mathbb{M}$ while interpolating the give...

Piecewise constant curvature soft actuators can generate various types of movements. These actuators can undergo extension, bending, rotation, twist, or a combination of these. Proprioceptive sensing provides the ability to track their movement or es...

We applied the Ramsey analysis to the sets of points belonging to Riemannian manifolds. The points are connected with two kinds of lines: geodesic and non-geodesic. This interconnection between the points is mapped into the bi-colored, complete Ramse...

A unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of eac...

The concircularity property of vector fields implies the geodesicity property, while the converse of this statement is not true. The main objective of this note is to find conditions under which the concircularity and geodesicity properties of vector...

In this paper, we study centroids, orthocenters, circumcenters, and incenters of geodesic triangles in non-Euclidean geometry, and we discuss the existence of the Euler line in this context. Moreover, we give simple proofs of the existence of a total...

We give a proof of Cartan’s Theorem on totally geodesic submanifolds for real analytic manifolds endowed with a real analytic, torsion-free, affine connection. We apply the theorem to real analytic Hadamard manifolds and, more generally, to rea...

The geometric concept of geodesic completeness depends on the choice of the metric field or “metric frame”. We develop a frame-invariant concept of “generalised geodesic completeness” or “time completeness”. It is...

Curves constructed directly on point clouds are a core primitive in reverse engineering, product design, and point-based CAD; many workflows additionally require the curve to lie in a plane—e.g., as a section profile, inspection path, or design...

Over the last decade there has been a proliferation of glamping architecture. This study analyses the energy performance of geodesic domes for use in tourist glamping compared to more conventional prismatic architectural solutions. The energy analysi...

In this article, we introduce analogues of classic Euclidean bounds, including spherical caps, geodesic axis-aligned bounding boxes (AABBs), geodesic oriented bounding boxes (OBBs), and geodesic k-discrete oriented polytopes (k-DOPs). We also formula...

We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is pr...

In this paper, geometric structures on an open subset ${\displaystyle D\subseteq {\mathbb{R}}^2}$ are investigated such that the graphs associated with the solutions of some special functions to become geodesics. More precisely, we determine the Riemannian metric ${\displaystyle g}$...

This article introduces the concept of geodesic mappings of manifolds with idempotent pseudo-connections. The basic equations of canonical geodesic mappings of manifolds with completely idempotent pseudo-connectivity and semi-Riemannian manifolds wit...

The convex optimization problems have been considered by many researchers on geodesic spaces. In these problems, the resolvent operators play an important role. In this paper, we propose new resolvents on geodesic spaces, and we show that they have b...

We examine a causally specified geometric reference for forecasting a two-sided path event: whether the absolute cumulative log return from the forecast origin reaches 0.05 at any of the next 20 trading observations. The Geometric Curve Manifold (GCM...

In the present paper, we study geodesic mappings of special pseudo-Riemannian manifolds called $V_n\left(K\right)$ -spaces. We prove that the set of solutions of the system of equations of geodesic mappings on $V_n\left(K\right)$ -spaces forms a sp...

We investigate timelike and null geodesics within the rotating “time machine” spacetime proposed by Ralph, T.C.; et al. Phys. Rev. D 2020, 102, 124013. This is a rotating analogue of Alcubierre’s warp drive spacetime. We obtain...

Querying the geodesic distance field on a given smooth surface is a fundamental research pursuit in computer graphics. Both accuracy and smoothness serve as common indicators for evaluating geodesic algorithms. In this study, we argue that ensuring t...

This article gives an approach for establishing a surface family with a mutual geodesic curve in Galilean 3-space ${\mathbb{G}}_3$. Given a smooth space curve, we derive the sufficient and necessary condition for the given curve to be geodesic on it. Furthermore,...

We consider isofrequency pairing of geodesic orbits that share the same three orbital frequencies associated with ${\Omega }^{\widehat{r}}$, ${\Omega }^{\widehat{\phi }}$, and ${\Omega }^{\widehat{\omega }}$ in a particular region of parameter space around black string spacetime geometry. We study the effect of a compact ext...

Simple closed formulas for endpoint geodesics on Graßmann manifolds are presented. In addition to realizing the shortest distance between two points, geodesics are also essential tools to generate more sophisticated curves that solve higher ord...

In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a c...

With the advancement of service robot technology, the demand for higher boundary precision in indoor semantic segmentation has increased. Traditional methods of extracting Euclidean features using point cloud and voxel data often neglect geodesic inf...

In this paper, we study contact magnetic geodesics in a 3-dimensional Lie group G endowed with a left invariant almost cosymplectic structure. We distinguish the two cases: G is unimodular, and G is nonunimodular. We pay a careful attention to the sp...

Geodesic projection distances on statistical manifolds have been widely applied across various research fields. Nevertheless, the existing closed-form solution is only available for the Gaussian manifold. Multivariate elliptical distributions (MEDs)...