2015 **Abstract:** In this paper, we give one parameter families of extrinsic differential geometries on spacelike curves in Minkowski 4-space. We investigate the nonlinear properties of one parameter lightlike hypersurfaces. Meanwhile, the classification of singularities to one parameter lightlike hypersurfaces is considered by singularity theory. c ⃝2015 All rights reserved.

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“…In the present paper, we investigate one-parameter developable surfaces, which are related to the space curves, as a fundamental case for the research of the highest dimensional manifolds in Euclidean 3-space. We investigated the singularities of hypersurfaces in semi-Euclidean space [7][8][9][10]. However, at least to the best of our knowledge, there exists little literature concerning the singularities of one-parameter developable surfaces related to regular space curves in Euclidean space.…”

confidence: 99%

“…In the present paper, we investigate one-parameter developable surfaces, which are related to the space curves, as a fundamental case for the research of the highest dimensional manifolds in Euclidean 3-space. We investigated the singularities of hypersurfaces in semi-Euclidean space [7][8][9][10]. However, at least to the best of our knowledge, there exists little literature concerning the singularities of one-parameter developable surfaces related to regular space curves in Euclidean space.…”

confidence: 99%