A New Representation of Canal Surfaces with Split Quaternions in Minkowski 3-Space

Kocakuşaklı, Erdem; Tuncer, O. Oğulcan; Gök, Ísmaíl; Yaylı, Yusuf

doi:10.1007/s00006-016-0723-5

Cited by 17 publications

(9 citation statements)

References 20 publications

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“…Lately, in [13], the authors consider the new approach to canal surfaces. Also in [2] and [9], the authors study canal surfaces with quaternions.…”

Section: Introductionmentioning

confidence: 99%

Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame

Uçum

2021

International Electronic Journal of Geometry

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In this paper, we obtain the parametrization of the canal surfaces whose center curves are the hyperbolic curves on the hyperbolic space H 2 in E 3 1 . The parametrization of the canal surface is expressed according to the hyperbolic frame given in [10]. Then, the parallel surface of this surface is studied. Also, we define the notion of the associated canal surface. Lastly, we give the geometric properties of these surfaces such that Weingarten surface, (X, Y )-Weingarten surface and linear Weingarten surface.

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“…Lately, in [13], the authors consider the new approach to canal surfaces. Also in [2] and [9], the authors study canal surfaces with quaternions.…”

Section: Introductionmentioning

confidence: 99%

Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame

Uçum

2021

International Electronic Journal of Geometry

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“…Many studies on quaternionic representations of surfaces have been achieved. [12][13][14][15][16][17] These studies have examined quaternionic expressions of surfaces such as constant slope and canal surfaces in Euclidean and Minkowski spaces.…”

Section: Introductionmentioning

confidence: 99%

Surface‐dependent growth kinematics in euclidean 3‐space

Öncül

Özdemi̇r

Gök

2020

Math Methods in App Sciences

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In this paper, we investigate the surface‐dependent growth model in Euclidean 3‐space. The surface‐dependent model is developed for modeling the kinematics of surface growth for objects that can be generated by the curves on the surface, such as parasites and plants. This paper includes two main purposes for this model. The first is to parameterize this model using quaternions and homothetic motions, while expressing matrix representations of the surface‐dependent growth model. The second one is to construct the surface‐dependent growth model by using the growth velocity components related to the Darboux frame at each point of the generating curve. Moreover, to support the theory studied in the paper, various examples are illustrated.

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“…In recent papers, split quaternions have been widely used . For example, Aslan and Kocakuşaklı studied canal surfaces with split quaternions in [1], [9]. Aslan gave quaternionic shape operator in [2], and Tunçer studied circular surfaces with split quaternions.…”

Section: Introductionmentioning

confidence: 99%

On Bäcklund Transformations With Split Quaternions

Sariaydin

2020

FU Math Inform

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The present paper deals with the introduction of Bäcklund Transformations with split quaternions in Minkowski space. Firstly, we tersely summarized the basic concepts of split quaternion theory and Bishop Frames of non-null curves in Minkowski space. Then, for Bäcklund transformations defined with each case of non-null curves, we give relationships between Bäcklund transformations and split quaternions. It is also presented some special propositions for transformations constructed with split quaternions. At the end, results obtained with the mathematical model have been evaluated.

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A New Representation of Canal Surfaces with Split Quaternions in Minkowski 3-Space

Cited by 17 publications

References 20 publications

Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame

Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame

Surface‐dependent growth kinematics in euclidean 3‐space

On Bäcklund Transformations With Split Quaternions

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