Normal and Spherical Curves in Dual Space

Ruled Weingarten Surfaces Related to Dual Spherical Curves

We study ruled surfaces in R3 which are obtained from dual spher- ical indicatrix curves of dual Frenet vector fields. We find the Gaussian and mean curvatures of the ruled surfaces and give some results of being Wein- garten surface.

Spherical T-duality II: An infinity of spherical T-duals for non-principal SU(2)-bundles

Recently we initiated the study of spherical T-duality for spacetimes that are principal SU(2)-bundles. In this paper, we extend spherical T-duality to spacetimes that are oriented non-principal SU(2)-bundles. There are several interesting new examples in this case and a new phenomenon appearing in the non-principal case is the existence of infinitely many spherical T-duals.

Spherical T-Duality and the spherical Fourier-Mukai transform

In earlier papers, we introduced spherical T-duality, which relates pairs of the form $(P,H)$ consisting of an oriented $S^3$-bundle $P\rightarrow M$ and a 7-cocycle $H$ on $P$ called the 7-flux. Intuitively, the spherical T-dual is another such pair $(\hat P, \hat H)$ and spherical T-duality exchanges the 7-flux with the Euler class, upon fixing the Pontryagin class and the second Stiefel-Whitney class. Unless $\mathrm{dim}(M)\leq 4$, not all pairs admit spherical T-duals and the spherical T-duals are not always unique. In this paper, we define a canonical Poincaré virtual line bundle $\mathc…

拓扑球面T对偶——来自更高次$H$-通量的维度变化

Topological Spherical T-duality -- Dimension change from higher degree $H$-flux

本文将拓扑球面T对偶进一步推广至配备任意次数闭奇形式的$S^{2n-1}$-丛，证明其T对偶存在且对偶空间扭曲上同调同构，并引入相容的Courant代数胚版本。

On the Mannheim Surface Offsets

In this paper, we study Mannheim surface offsets in dual space. By the aid of the E. Study Mapping, we consider ruled surfaces as dual unit spherical curves and define the Mannheim offsets of the ruled surfaces by means of dual geodesic trihedron (dual Darboux frame). We obtain the relationships between the invariants of Mannheim ruled surfaces. Furthermore, we give the conditions for these surface offset to be developable. Furthermore, we obtained that the dual spherical radius of curvature of offset surface is equal to dual offset angle.

Polygons of the Lorentzian plane and spherical simplexes

It is known that the space of convex polygons in the Euclidean plane with fixed normals, up to homotheties and translations, endowed with the area form, is isometric to a hyperbolic polyhedron. In this note we show a class of convex polygons in the Lorentzian plane such that their moduli space, if the normals are fixed and endowed with a suitable area, is isometric to a spherical polyhedron. These polygons have an infinite number of vertices, are space-like, contained in the future cone of the origin, and setwise invariant under the action of a linear isometry.