1-Lightlike surfaces in semi-Euclidean 4-space with index two

Volume 9, Issue 5, pp 3127--3146 http://dx.doi.org/10.22436/jnsa.009.05.103

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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.

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Keywords

• Hermite-Hadamard's inequality
• Hermite-Hadamard's inequality
• anti de Sitter space
• Legendrian singularity.

MSC

•  47H09
•  47H10

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