Surface Pencil Pair Interpolating Bertrand Pair as Common Asymptotic Curves in Euclidean 3-Space

Article Mathematics, Applied

Singularities of Non-lightlike Developable Surfaces in Minkowski 3-Space

Sahar H. Nazra et al.

Summary: In this work, the singularities of non-lightlike developable surfaces in Minkowski 3-space R-1(3) are classified using the Bishop frame. The necessary and sufficient conditions for spacelike developable surfaces to be cylinders, cones, or tangent surfaces are analyzed. Finally, some representative examples are provided.

MEDITERRANEAN JOURNAL OF MATHEMATICS (2023)

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Article Multidisciplinary Sciences

Singularity Properties of Spacelike Circular Surfaces

Areej A. Almoneef et al.

Summary: The aim of this paper is to study spacelike circular surfaces and singularities in Minkowski 3-space E-1(3). It is shown that a spacelike circular surface with a stationary radius can be generated by a movable Lorentzian circle following a non-null curve, which acts as the spine curve. The paper presents the representation and geometric properties of spacelike circular surfaces, including singularities and striction curves, in contrast to ruled surfaces. Additionally, a new type of spacelike circular surface, named spacelike roller coaster surface, is introduced and supported by examples.

SYMMETRY-BASEL (2023)

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Article Mathematics, Applied

Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean 3-space

Yanlin Li et al.

Summary: In this paper, we investigate the singularities on a non-developable ruled surface in Euclidean 3-space using Blaschke's frame. Our study confirms the existence of singular points on this type of surface and employs singularity theory technique to analyze these singularities. We also provide an example to validate and demonstrate our main findings.

AIMS MATHEMATICS (2023)

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Article Physics, Mathematical