Spacelike Parallels and Evolutes in Minkowski pseudo-spheres
Spacelike Parallels and Evolutes in Minkowski pseudo-spheres
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DOI：
10.1016/j.geomphys.2007.01.008
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发表时间：
2006-01
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影响因子：
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通讯作者：
S. Izumiya;Masatomo Takahashi
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文献类型：
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作者：
S. Izumiya;Masatomo Takahashi
我们考虑Minkowski伪球面（双曲空间，de Sitter空间和光锥）中类空超曲面上的外微分几何。在以前的论文[S. Izumiya，Legendrian dualities and spacelike hypersurfaces in the lightcone，Preprint]我们已经证明了伪球面之间的基本Legendrian对偶定理。我们利用勒让德对偶定理定义了类空平行线。这个定义统一了伪球面中类空超曲面的平行线的概念。我们也定义渐屈线为类空平行线的奇点轨迹。这些概念的拉格朗日或Legendrian奇点理论的应用进行了研究。我们考虑对应于类空平行线或渐屈线奇点的非奇异类空超曲面的几何性质。
We consider extrinsic differential geometry on spacelike hypersurfaces in Minkowski pseudo-spheres (hyperbolic space, de Sitter space and the lightcone). In the previous paper [S. Izumiya, Legendrian dualities and spacelike hypersurfaces in the lightcone, Preprint] we have shown a basic Legendrian duality theorem between pseudo-spheres. We define the spacelike parallels by using the basic Legendrian duality theorem. This definition unifies the notions of parallels of spacelike hypersurfaces in pseudo-spheres. We also define the evolute as the locus of singularities of the spacelike parallels. These notions are investigated as applications of Lagrangian or Legendrian singularity theory. We consider geometric properties of non-singular spacelike hypersurfaces corresponding to singularities of spacelike parallels or evolutes.