In this paper, we confine the trajectory of geometrical particles to the de Sitter three-dimensional space–time, we model geometrical particles as spacelike tachyons. Using the Legendrian duality theory of pseudo-spheres and contact manifolds theory we establish the dual relationships between spacelike moving trajectory of geometrical particles and future nullcone hypersurfaces.

中文翻译：

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null de Sitter 3-sphere 中与曲线相关的几何粒子和二元性

在本文中，我们将几何粒子的轨迹限制在德西特三维时空，我们将几何粒子建模为类空间快子。使用Legendrian伪球对偶理论和接触流形理论，我们建立了几何粒子的类空间运动轨迹与未来零锥超曲面之间的对偶关系。