In this paper, homothetical and translation lightlike graphs, which are generalizations of homothetical and translation lightlike hypersurfaces are investigated in the semi-Euclidean space $ \mathbb{R}_{q}^{n+2} $, respectively. We prove that all homothetical and all translation lightlike graphs are locally the hyperplanes. According to this fact, both of these graphs are minimal.
Citation: Derya Sağlam. Minimal homothetical and translation lightlike graphs in $ \mathbb{R} _{q}^{n+2} $[J]. AIMS Mathematics, 2022, 7(9): 17198-17209. doi: 10.3934/math.2022946
In this paper, homothetical and translation lightlike graphs, which are generalizations of homothetical and translation lightlike hypersurfaces are investigated in the semi-Euclidean space $ \mathbb{R}_{q}^{n+2} $, respectively. We prove that all homothetical and all translation lightlike graphs are locally the hyperplanes. According to this fact, both of these graphs are minimal.
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Derya Sağlam. Minimal homothetical and translation lightlike graphs in $ \mathbb{R} _{q}^{n+2} $[J]. AIMS Mathematics, 2022, 7(9): 17198-17209. doi: 10.3934/math.2022946
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