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2-Ruled hypersurfaces in Minkowski 4-space and their constructions via octonions
  • Ameth Ndiaye,
  • Zehra Özdemir
Ameth Ndiaye
Université Cheikh Anta Diop de Dakar

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Zehra Özdemir
Amasya University
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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
29 May 2022Submitted to Mathematical Methods in the Applied Sciences
30 May 2022Submission Checks Completed
30 May 2022Assigned to Editor
08 Sep 2022Reviewer(s) Assigned
10 Jun 2023Review(s) Completed, Editorial Evaluation Pending
12 Jun 2023Editorial Decision: Revise Major
09 Jul 20231st Revision Received
16 Jul 2023Submission Checks Completed
16 Jul 2023Assigned to Editor
16 Jul 2023Review(s) Completed, Editorial Evaluation Pending
17 Jul 2023Reviewer(s) Assigned
27 Oct 2023Editorial Decision: Accept