On lightlike hypersurfaces and lightlike focal sets of null Cartan curves in Lorentz-Minkowski spacetime

Volume 8, Issue 5, pp 628--639 http://dx.doi.org/10.22436/jnsa.008.05.15

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Authors

Xinran Liu - 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. - College of Mathematics, Jilin University, Changchun, 130012, P. R. China.

Abstract

In this paper, as a type of event horizons in astrophysics, a class of lightlike hypersurfaces that is generated by null curves will be investigated and discussed. Based on discussions of the properties of the local differential geometry of null curves and singularity theory, we provide classifications of the singularities of lightlike hypersurfaces and lightlike focal sets. In addition, we reveal the facts that the types of these singularities and the order of contact between a null Cartan curve and a pseudosphere are related closely to null Cartan curvatures. Finally, examples of lightlike hypersurfaces and lightlike focal set are used to demonstrate our theoretical results.

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Keywords

• null Cartan curve
• lightlike hypersurface
• singularity

MSC

•  57R45
•  53B30
•  53B50

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