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In this paper we investigate the differential geometry of 1-lightlike submanifolds in anti-de Sitter n -space as an application of the theory of Legendrian singularities. Based on some theory of lightlike submanifolds, we also introduce the notion of 1-lightlike horospherical Gauss curvature, which is important for us to study the singularities of 1-lightlike horospherical hypersurfaces. Moreover, we discuss the related geometric property of 1-lightlike horospherical hypersurfaces in anti-de Sitter n -space.
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Wang et al. (2013) studied this question.
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