Singularities for normal hypersurfaces of de Sitter timelike curves in Minkowski 4-space

Yongqiao Wang and Donghe Pei

Journal of Singularities
volume 12 (2015), 207-214

Received 16 June 2015. Received in revised form 7 January 2015.

DOI: 10.5427/jsing.2015.12o

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In this paper, we consider the normal hypersurfaces associated with timelike curves in Minkowski 4-space which are confined in de Sitter 3-space. We classify the generic singularities of the normal hypersurfaces, which are cuspidal edges, swallowtails and butterflies. And reveal the relationships between these singularities and the Lorentzian invariants of timelike curves by applying the singularity theory.


timelike curves, de Sitter 3-space, normal hypersurfaces, Lorentzian invariants

Mathematical Subject Classification:

53A35, 58C27, 58C28

Author(s) information:

Yongqiao Wang Donghe Pei
School of Mathematics and Statistics School of Mathematics and Statistics
Northeast Normal University Northeast Normal University
Changchun, 130024, P.R.China Changchun, 130024, P.R.China
email: email: