Singularities of Null Hypersurfaces of Pseudonull Curves

Cui, Xiupeng; Pei, Donghe

doi:10.1155/2015/502789

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…(A) By definition, OD is a cylinder if and only if D ∧ D = 0. Because D ∧ D = 0 if and only if ε(s) ≡ 0, it means that (1) is equivalent to (2). Suppose that (3) holds; there exists a vector…”

Section: Osculating Developable Surfacesmentioning

confidence: 99%

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Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves

Wang

Yang

et al. 2022

Symmetry

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In this paper, we focus on a developable surface tangent to a timelike surface along a curve in Minkowski 3-space, which is called the osculating developable surface of the timelike surface along the curve. The ruling of the osculating developable surface is parallel to the osculating Darboux vector field. The main goal of this paper is to classify the singularities of the osculating developable surface. To this end, two new invariants of curves are defined to characterize these singularities. Meanwhile, we also research the singular properties of osculating developable surfaces near their lightlike points. Moreover, we give a relation between osculating Darboux vector fields and normal vector fields of timelike surfaces along curves from the viewpoint of Legendrian dualities. Finally, some examples with symmetrical structures are presented to illustrate the main results.

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Section: Osculating Developable Surfacesmentioning

confidence: 99%

“…Minkowski space, which is regarded as the mathematical setting for the theory of relativity, has been studied by both physicists and differential geometers in large amounts; see, for example, [1][2][3][4][5][6][7]. As is known to all, there exist spacelike surfaces, timelike surfaces and lightlike surfaces in Minkowski 3-space.…”

Section: Introductionmentioning

confidence: 99%