Bicomplex extensions of zero mean curvature surfaces in R2,1 and R2,2
Bicomplex extensions of zero mean curvature surfaces in R2,1 and R2,2
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R2,1 和 R2,2 中零平均曲率曲面的双复形延拓
DOI：
10.1016/j.geomphys.2018.12.017
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发表时间：
2019
影响因子：
1.5
通讯作者：
Kato Shin
中科院分区：
文献类型：
--
作者：
Hashimoto Kaname;Kato Shin
本文利用双复数的方法，构造了CN中具有各种标准度量的零平均曲率复曲面，每一个标准度量的类型都从正定转变为中性.通过将它们作为双复扩张，我们描述了R2，1和R2，2中零平均曲率的真实的曲面的折叠奇点与变型之间的对应关系。特别是，我们表明，任何折叠奇点由双复扩张的分支点。我们还表明，跨越类光线段的类型变化发生在一个不完整的结束上的折叠奇点。
In this paper, we construct zero mean curvature complex surfaces in C N with a various type of standard metric, each of which changes its type from positive definite to neutral, by means of bicomplex numbers. By applying them as bicomplex extensions, we describe the correspondence between fold singularities and type-changing of zero mean curvature real surfaces in R 2, 1 and R 2, 2. In particular, we show that any fold singularity consists of branch points of the bicomplex extension. We also show that type-changing across a lightlike line segment occurs on an incomplete end on a fold singularity.