论文标题
Minkowski 4空间中的2条超曲面及其通过八座的结构
2-Ruled hypersurfaces in Minkowski 4-space and their constructions via octonions
论文作者
论文摘要
在本文中，我们在Minkowski 4-Space $ \ Mathbb {e}^4_1 $中定义了三种类型的2条式超曲面。我们获得了1型和2型2型超曲面的高斯和平均曲率，以及有关其最小值的一些特征。我们还与$ \ Mathbb {e}^4_1 $中的这些类型的2条式超曲面的第一个Laplace-Beltrami操作员打交道。此外，本文的重要性是，通过在$ \ mathbb {e}^4_1 $中使用octonions对这些表面的定义。因此，这是一个新想法，并将纸制成原始想法。我们给出了由八元构建的2条超脸的示例，我们使用枫树程序可视化图像的投影。此外，光纤可以定义为嵌入4维Minkowski Space $ \ Mathbb {E}^4_1 $的一维对象。因此，作为一个讨论，我们通过四维Minkowski空间中的2条式超曲面来研究沿光纤线性光波的几何演化。
In this paper, we define three types of 2-Ruled hypersurfaces in the Minkowski 4-space $\mathbb{E}^4_1$. We obtain Gaussian and mean curvatures of the 2-ruled hypersurfaces of type-1 and type-2, and some characterizations about its minimality. We also deal with the first Laplace-Beltrami operators of these types of 2-Ruled hypersurfaces in $\mathbb{E}^4_1$. Moreover, the importance of this paper is that the definition of these surfaces by using the octonions in $\mathbb{E}^4_1$. Thus, this is a new idea and make the paper original. We give an example of 2-ruled hypersurface constructed by octonion and we visualize the projections of the images with MAPLE program. Furthermore, the optical fiber can be defined as a one-dimensional object embedded in the 4-dimensional Minkowski space $\mathbb{E}^4_1$. Thus, as a discussion, we investigate the geometric evolution of a linearly polarized light wave along an optical fiber by means of the 2-ruled hypersurfaces in a four-dimensional Minkowski space.
