New approach to Bäcklund transformations for a curve and its pedal curve

Sariaydin, Muhammed T.; Körpınar, Talat

doi:10.1007/s13370-018-0636-7

Cited by 4 publications

(2 citation statements)

References 9 publications

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“…Thus, the orthogonal frame   ,, T N B is called the modified orthogonal frame at nonzero points of the curvature  [11]. It is easily seen that for (9) Let , be the standard inner product of the Euclidean space 3 E , then the following equalities are given 2 ,…”

Section: T T N N B B T N T B N B (6)mentioning

confidence: 99%

“…In the three dimensional Euclidean space, many studies have been conducted with the involute-evolute curve pair [2][3][4]. Recently, these studies focused on the examination of their characteristic properties according to different frames [5][6][7][8][9][10]. Several researchers studied the problem of analytic space curves which their curvatures have discrete zero points.…”

Section: Introductionmentioning

confidence: 99%

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Involute-Evolute Curves According to Modified Orthogonal Frame

Azak

2021

J. Sci. Arts

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In this paper, the involute-evolute curve concept has been deﬁned according to two type modiﬁed orthogonal frames at non-zero points of curvature and torsion in the Euclidean space E^3 , respectively. Later, the characteristic theorems related to the distance between the corresponding points of these curves have been given. Besides, the relations have been found between the curvatures and also torsions of the two type the involute-evolute modiﬁed orthogonal pairs.

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Section: T T N N B B T N T B N B (6)mentioning

confidence: 99%