Abstract
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