Papers by maryam aldossary
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Symmetry
The approach of the paper is on spacelike circular surfaces in the Minkowski 3-space. A spacelike... more The approach of the paper is on spacelike circular surfaces in the Minkowski 3-space. A spacelike circular surface is a one-parameter family of Lorentzian circles with a fixed radius regarding a non-null curve, which acts as the spine curve, and it has symmetrical properties. In the study, we have parametrized spacelike circular surfaces and have provided their geometric and singularity properties such as Gaussian and mean curvatures, comparing them with those of ruled surfaces and the classification of singularities. Furthermore, the conditions for spacelike roller coaster surfaces to be flat or minimal surfaces are obtained. Meanwhile, we support the results of the approach with some examples.
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AIMS Mathematics
In this paper using the Blaschke approach we generalized the Bertrand curves to spacelike ruled a... more In this paper using the Blaschke approach we generalized the Bertrand curves to spacelike ruled and developable surfaces. It is proved that, every spacelike ruled surface have a Bertrand offset if and only if an equation should be fulfilled among their dual integral invariants. Consequently, some new relationships and theorems for the developability of the Bertrand offsets of spacelike ruled surfaces are outlined.
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Bollettino dell'Unione Matematica Italiana, 2015
This work examines some classical results of Bertrand curves for ruled and developable surfaces u... more This work examines some classical results of Bertrand curves for ruled and developable surfaces using the E. Study’s dual line coordinates. In particular, a developable surface can have a developable Bertrand offset if a linear equation holds between the curvature and torsion of its edge of regression. From this result many of the classical results of closed space curve follow rather simply. Finally, an example of application is introduced and explained in detail.
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International Journal of Mathematics and Statistics, 2013
Let M and M* are two timelike surfaces in Minkowski 3-Space R^3_1. If there exists a spacelike (t... more Let M and M* are two timelike surfaces in Minkowski 3-Space R^3_1. If there exists a spacelike (timelike) Darboux line congruence between each point of M and M*, then the surfaces are timelike Weingarten surfaces. It turns out their Tschebyscheff angles are solutions of the Sinh-Gordon equation and the surfaces are related to each other by Backlund’s transformation. Finally, a method to construct new timelike Weingarten surface has been found.
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We study ruled surfaces with lightlike ruling in Minkowski 3-space which are said to be null-scro... more We study ruled surfaces with lightlike ruling in Minkowski 3-space which are said to be null-scrolls. Even that the result is a consequence of some well-known results involving the Gauss map, we give another approach to classify all null-scrolls under the condition where is the Laplace operator with respect to the first fundamental form and the set of 3 real matrices.
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The main goal of this paper is to investigate motion of parallel curves and surfaces in Euclidean... more The main goal of this paper is to investigate motion of parallel curves and surfaces in Euclidean 3-space R3. The characteristic properties for such objects are given. The geometric quantities are described. Finally, the evolution equations of the curvatures and the intrinsic geometric formulas are derived. keywords: Curvature, Evolution, Motion, Parallel curves, Parallel surfaces.
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Papers by maryam aldossary