Related papers: Holomorphic horospherical duality "sphere-cone"
A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables…
In this paper we study a class of convex sets which are called closed pseudo-cones and study a new duality of this class. It turns out that the duality characterizes closed pseudo-cones and is essentially the only possible abstract duality…
We introduce a combinatorial theory of horospherical stacks which is motivated by the work of Geraschenko and Satriano on toric stacks. A horospherical stack corresponds to a combinatorial object called a stacky coloured fan. We give many…
We discuss meromorphic functions on the complex plane which are Brody curves regarded as holomorphic maps to P_1, i.e., which have bounded spherical derivative.
A simple derivation of the classical solutions of a nonlinear model describing a harmonic oscillator on the sphere and the hyperbolic plane is presented in polar coordinates. These solutions are then related to those in cartesian…
We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.
We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification…
We describe the duality between different geometries which arises by considering the classical and quantum harmonic map problem. To appear in ``Essays on Mirror Manifolds II''.
For complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the…
In this paper we discuss some mathematical aspects of the horizon wave-function formalism, also known in the literature as horizon quantum mechanics. In particular, first we review the structure of both the global and local formalism for…
This article is an exposition and elaboration of recent work of the first author on spinors and horospheres. It presents the main results in detail, and includes numerous subsidiary observations and calculations. It is intended to be…
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…
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…
This is a survey on coarse geometry with an emphasis on coarse homology theories.
We construct large families of harmonic morphisms which are holomorphic with respect to Hermitian structures by finding heierarchies of Weierstrass-type representations. This enables us to find new examples of complex-valued harmonic…
We present the formalism for calculating the femtoscopic correlation function directly in spherical harmonics. The numerator and denominator are stored as a set of one-dimensional histograms representing the spherical harmonic…
The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the…
In this article we study polyharmonic curves of constant curvature where we mostly focus on the case of curves on the sphere. We classify polyharmonic curves of constant curvature in three-dimensional space forms and derive an explicit…
The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an…
Spherical $t$-designs are finite point sets on the unit sphere that enable exact integration of polynomials of degree at most $t$ via equal-weight quadrature. This concept has recently been extended to spherical $t$-design curves by the use…