Pseudo‐spherical evolutes of lightlike loci on mixed type surfaces in Minkowski 3‐space
Pseudo‐spherical evolutes of lightlike loci on mixed type surfaces in Minkowski 3‐space
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DOI：
10.1002/mma.8987
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发表时间：
2022-12
影响因子：
2.9
通讯作者：
Yongqiao Wang;Lin Yang;Yuan Chang;Haiming Liu
中科院分区：
文献类型：
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作者：
Yongqiao Wang;Lin Yang;Yuan Chang;Haiming Liu
在闵可夫斯基三维空间中具有非空类时点、类光点和类空间点的曲面是一个混合型曲面。混合型曲面具有一个特征变化度规，其类光点可以看作是该度规的奇点。本文研究了混合型表面上类光轨迹的拟球面演化曲线的奇异性。利用奇异性理论对拟球面演化体的一般奇异性进行了分类。这些奇异点与类光轨迹和模型子流形之间的接触密切相关。我们还展示了伪球面演化曲线、类光轨迹和达布向量之间的Legendrian对偶性。此外，从开图胚的角度研究了伪球面演化曲线的奇异性。最后，通过算例对理论结果进行了验证。
A surface with nonempty timelike, lightlike, and spacelike points in Minkowski 3‐space is a mixed type surface. The mixed type surface has a signature‐changing metric, and its lightlike points can be seen as singularities of such metric. In this paper, we study singular properties of pseudo‐spherical evolutes of lightlike loci on mixed type surfaces. We classify the generic singularities of pseudo‐spherical evolutes by the singularity theory. These singularities and the contact between lightlike loci and model submanifolds are closely associated. We also show the Legendrian duality among pseudo‐spherical evolutes, lightlike loci, and Darboux vectors. Moreover, the singularities of pseudo‐spherical evolutes are studied from the viewpoint of opening map‐germ. Finally, we give an example to demonstrate the theoretical results.