Related papers: A note on the geodesic normal distribution on the …
This paper is concerned with the study of a circular random distribution called geodesic Normal distribution recently proposed for general manifolds. This distribution, parameterized by two real numbers associated to some specific location…
We consider geodesics on the surfaces obtained by weak deformations of the standard 2D-sphere. The dynamics of a particle on the surface can be asymptotically described by the averaged evolution of the particle's angular momentum. It is…
Elliptically contoured distributions generalize the multivariate normal distributions in such a way that the density generators need not be exponential. However, as the name suggests, elliptically contoured distributions remain to be…
A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular…
A new potential is presented for spherical galaxies. The technique of the construction of our model is similar to that given by An and Evans. In a special case, its mass density becomes a special one of the Hernquist model. Another special…
The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion.…
It is shown that unlike the perfect fluid case, anisotropic fluids (principal stresses unequal) may be geodesic, without this implying the vanishing of (spatial) pressure gradients. Then the condition of vanishing four acceleration is…
The purpose of this paper is to study transport equations on the unit tangent bundle of closed oriented Riemannian surfaces and to connect these to the transport twistor space of the surface (a complex surface naturally tailored to the…
Let S be a triangulated 2-sphere with fixed triangulation T. We apply the methods of thin position from knot theory to obtain a simple version of the three geodesics theorem for the 2-sphere [5]. In general these three geodesics may be…
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
The Thurston metric on Teichmuller space, first introduced by W. P. Thurston is an asymmetric metric on Teichmuller space defined by $d_{Th}(X,Y) = \frac12 log\sup_{\alpha} \frac{l_{\alpha}(Y)}{l_{\alpha}(X)}$. This metric is geodesic, but…
The non isotropic noncentral elliptical shape distributions via pseudo-Wishart distribution are founded. This way, the classical shape theory is extended to non isotropic case and the normality assumption is replaced by assuming a…
We present a new, elementary way to obtain axially symmetric Gaussian processes on the sphere, in order to accommodate for the directional anisotropy of global climate data in geostatistical analysis.
We obtain formulae for the expected number and height distribution of critical points of smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense…
Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are…
We consider the classical ballistic dynamics of massless electrons on the conducting surface of a three-dimensional topological insulator, influenced by random variations of the surface height. By solving the geodesic equation and the…
In this paper, we generalize the classification of geodesic orbit spheres from Riemannian geometry to Finsler geometry. Then we further prove if a geodesic orbit Finsler sphere has constant flag curvature, it must be Randers. It provides an…
We exhibit orbits of the geodesic flow on a hyperbolic surface with at least one cusp such that every tubular neighborhood contains uncountably many distinct geodesic flow orbits. The proof relies on new phenomena, namely the existence of…
We asymptotically estimate the variance of the number of lattice points in a thin, randomly rotated annulus lying on the surface of the sphere. This partially resolves a conjecture of Bourgain, Rudnick, and Sarnak. We also obtain estimates…
We consider the evolution of a compact segment of an analytic curve on the unit tangent bundle of a finite volume hyperbolic $n$-manifold under the geodesic flow. Suppose that the curve is not contained in a stable leaf of the flow. It is…