Related papers: New deformations on spherical curves and \"Ostlund…

We discuss $\beta$-deformed geometries on two types of $T^3$'s where the direction along the third coordinate is not orthogonal to the direction along the second coordinate or the direction along the first coordinate. We show that the…

In this paper, I will show how to use $\beta$-deformations to deal with dual flatness of $(\alpha,\beta)$-metrics. It is a natural continuation of the research on dually flat Randers metrics(see arxiv:1209.1150). $\beta$-deformations is a…

We consider curves $\gamma : [0, 1]\to\mathbb{R}^3$ endowed with an adapted orthonormal frame $r : [0, 1]\to SO(3)$. We are interested in the cases where the frame is constrained, in the sense that one of its `curvatures' (i.e.,…

An $(\alpha,\beta)$-metric is defined by a Riemannian metric and $1$-form. In this paper, we investigate the known characterization for $(\alpha,\beta)$-metrics of isotropic S-curvature. We show that such a characterization should hold in…

We have studied volumes of the 3-cycle and the compact 5-volumes for the $\beta$ transformed geometry and it comes out to be decreasing except one choice for which the torus do not stay inside the 3-cycle and ``5-cycle.'' There are 3…

Using an angular momentum projected single particle basis, a pnQRPA approach is used to study the $2\nu\beta\beta$ properties of ten isotopes, exhibiting various quadrupole deformations. The mother and daughter nuclei exhibit different…

This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic…

Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…

We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical…

In this paper, we study the deformations of curves in the projective 3-space $\mathbb P^3$ (space curves), one of the most classically studied objects in algebraic geometry. We prove a conjecture due to J. O. Kleppe (in fact, a version…

In this paper, we propose a new procedure to deform spectral triples and their quantum isometry groups. The deformation data are a spectral triple $(\mathcal A,\mathcal H, D)$, a compact quantum group $\mathbb G$ acting algebraically and by…

Let $F$ be an algebraically closed field. We show that if a quantum formal deformation $A$ of a commutative domain $A_0$ over $F$ is a PI algebra, then $A$ is commutative if ${\rm char}(F)=0$, and has PI degree a power of $p$ if ${\rm…

This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of (0,-2)-curves on threefolds, or…

A new class of deformation of the matrix model of M-theory is considered. The deformation is analogous to the so-called $\b$-deformation of $D=3+1$, $\mN=4$ Super Yang-Mills theory, which preserves the conformal symmetry. It is shown that…

In this paper we deal with curves with degeneration degree two in pseudo-Euclidean spaces of index two. We characterize Bertrand curves. We show a correspondence between the evolute of a null curve and the involute of a certain spacelike…

We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.

Third order equations, which describe spherical surfaces (ss) or pseudospherical surfaces (pss), of the form \[ \nu\,z_{t}-\lambda\,z_{xxt}=A(z,z_{x},z_{xx})\,z_{xxx}+B(z,z_{x},z_{xx}) \] with $\nu$, $\lambda$ $\in$ $\mathbb{R}$,…

A closed Riemann surface $S$ (of genus at least one) is called an origami curve if it admits a non-constant holomorphic map $\beta:S \to E$ with at most one branch value, where $E$ is a genus one Riemann surface. In this case, $(S,\beta)$…

The unified $ (p,q; \alpha,\gamma, l)$-deformation of a number of well-known deformed oscillator algebras is introduced.The deformation is constructed by imputing new free parameters into the structure functions and by generalizing the…

Theoretical errors in the extraction of alpha from B -> pi^+ pi^-, rho^+ rho^-, rho pi decays are usually given in terms of upper bounds on alpha_eff-alpha obtained from isospin or from SU(3) relations, where alpha_eff is measured through…