Ruled surfaces with timelike rulings

Abdel-All, Nassar H.; Abdel-Baky, Rashad A.; Hamdoon, Fathi M.

doi:10.1016/s0096-3003(02)00664-1

Cited by 19 publications

(24 citation statements)

References 1 publication

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“…According to the geodesic theory in [1], the curve on the surface S is a geodesic if only if the principal normal N (s) of the curve and the normal (s; t 0 ) of the surface S at any point on the curve are parallel to each other. Thus, for all…”

Section: Surfaces With a Common Pseudo Null Geodesic Curve In E 3mentioning

confidence: 99%

On surfaces with common pseudo null geodesic in Minkowski 3-space

Öztürk

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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C o m m u n . Fa c . S c i. U n iv . A n k . S é r. A 1 M a th . S ta t. Vo lu m e 6 6 , N u m b e r 1 , P a g e s 2 2 9 -2 4 1 (2 0 1 7 ) D O I: 1 0 .1 5 0 1 / C o m m u a 1 _ 0 0 0 0 0 0 0 7 9 2 IS S N 1 3 0 3 -5 9 9 1 ON SURFACES WITH COMMON PSEUDO NULL GEODESIC IN MINKOWSKI 3-SPACE UFUK OZTURKAbstract. The problem of constructing a family of parametric surfaces from a given pseudo null curve using the Frenet trihedron frame of the curve in the Minkowski 3-space is studied. The necessary and su¢ cient conditions for the given pseudo null curve to be a common geodesic of the parametric surface are derived. As a member of the family, considered a ruled surface with a pseudo null directrix, and some corollaries on the ruled surface are given. Also, some examples are given to show the family of surfaces with a common pseudo null geodesic.

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Section: Surfaces With a Common Pseudo Null Geodesic Curve In E 3mentioning

confidence: 99%

On surfaces with common pseudo null geodesic in Minkowski 3-space

Öztürk

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…(3) (see [1,14]). If , , 0 dk q dq = , then the normal vectors are collinear at all points of the same ruling and at the nonsingular points of the surface N , the tangent planes are identical.…”

Section: Differential Geometry Of the Ruled Surfaces In Minkowski 3-smentioning

confidence: 99%

“…i) If the central normal vector h is spacelike and q is timelike, then the ruled surface N is said to be of type 1 N − . ii) If the central normal vector h and the ruling q are both spacelike, then the ruled surface N is said to be of type 1 N + . iii) If the central normal vector h is timelike and the ruling q is spacelike, then the ruled surface N is said to be of type 2 N + [9,19].…”

Section: Differential Geometry Of the Ruled Surfaces In Minkowski 3-smentioning

confidence: 99%

On the Developable Mannheim Offsets of Timelike Ruled Surfaces

Önder

Uğurlu

2014

Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.

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In this paper, using the classifications of timelike and spacelike ruled surfaces, we study the Mannheim offsets of timelike ruled surfaces in Minkowski 3-space. First, we define the Mannheim offsets of a timelike ruled surface by considering the Lorentzian casual character of the offset surface. We obtain that the Mannheim offsets of a timelike ruled surface may be timelike or spacelike. Furthermore, we characterize the developable of Mannheim offset of a timelike ruled surface by the derivative of the conical curvature κ of the directing cone.MSC: 53A10, 53B25, 53C50.

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“…There are many studies that interested with many properties of these surfaces in Euclidean space and some characterizations [5,11]. Furthermore, many geometers have studied some of the differential geometric concepts of the ruled surfaces in Minkowski space [1][2][3][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Studying on a Skew Ruled Surface by Using the Geodesic Frenet Trihedron of Its Generator

Hamdoon¹,

Omran²

2016

Korean Journal of Mathematics

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Abstract. In this article, we study skew ruled surfaces by using the geodesic Frenet trihedron of its generator. We obtained some conditions on this surface to ensure that this ruled surface is flat, II-flat, minimal, II-minimal and Weingarten surface. Moreover, the parametric equations of asymptotic and geodesic lines on this ruled surface are determined and illustrated through example using the program of mathematica.

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Ruled surfaces with timelike rulings

Cited by 19 publications

References 1 publication

On surfaces with common pseudo null geodesic in Minkowski 3-space

On surfaces with common pseudo null geodesic in Minkowski 3-space

On the Developable Mannheim Offsets of Timelike Ruled Surfaces

Studying on a Skew Ruled Surface by Using the Geodesic Frenet Trihedron of Its Generator

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