1-Lightlike surfaces in semi-Euclidean 4-space with index two
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Authors
Qiuyan Wang
- School of Mathematical Sciences, Harbin Normal University, Harbin, 150500, P. R. China.
Zhigang Wang
- School of Mathematical Sciences, Harbin Normal University, Harbin, 150500, P. R. China.
Abstract
By establishing some differential geometry theory on the 1-lightlike surfaces, we show several geometric
properties of the 1-lightlike surfaces which are completely different from non-lightlike surfaces. Based on
these theories, we consider the singularities of the 1-lightlike surfaces in semi- Euclidean 4-space with index
two as an application of the theory of Legendrian singularities. We characterize the singularities of the
1-lightlike focal hypersurfaces and describe the contacts between the 1-lightlike surface and the anti de
Sitter 3-sphere at singular points by employing Montaldi's theory. In addition, we also discuss the detailed
differential geometric properties of the 1-lightlike focal hypersurfaces in semi-Euclidean 4-space with index
2. Finally, an example will be proposed to explain our findings.
Share and Cite
ISRP Style
Qiuyan Wang, Zhigang Wang, 1-Lightlike surfaces in semi-Euclidean 4-space with index two, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 3127--3146
AMA Style
Wang Qiuyan, Wang Zhigang, 1-Lightlike surfaces in semi-Euclidean 4-space with index two. J. Nonlinear Sci. Appl. (2016); 9(5):3127--3146
Chicago/Turabian Style
Wang, Qiuyan, Wang, Zhigang. "1-Lightlike surfaces in semi-Euclidean 4-space with index two." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 3127--3146
Keywords
- Hermite-Hadamard's inequality
- Hermite-Hadamard's inequality
- anti de Sitter space
- Legendrian singularity.
MSC
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