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 . 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 . Moreover, the importance of this paper is the definition of these surfaces by using the octonions in . 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 . 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.