The 2-ruled hypersurfaces in Minkowski 4-space and their constructions via octonions

Abstract

In this paper, we define three types of 2-ruled hypersurfaces in the Minkowski 4-space E-1(4). 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 E-1(4). Moreover, the importance of this paper is the definition of these surfaces by using the octonions in E-1(4). Thus, this is a new idea and makes 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 four- dimensional Minkowski space E-1(4). 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.