Helicoidal surfaces in the 3-dimensional Lorentz-Minkowski space $E^3_1$ satisfying $\Delta^{III}r=Ar$

Senoussi, Bendehiba; Bekkar, Mohammed

doi:10.21099/tkbjm/1389972033

Cited by 3 publications

(4 citation statements)

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“…As a consequence, putting together with the results described above and theorems in [10], we have the following result: …”

Section: Equation (32) Can Be Written Asmentioning

confidence: 60%

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Helicoidal Surfaces of the Third Fundamental Form in Minkowski 3-Space

Choi¹,

Yoon²

2015

Bulletin of the Korean Mathematical Society

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Abstract. We study helicoidal surfaces with the non-degenerate third fundamental form in Minkowski 3-space. In particular, we mainly focus on the study of helicoidal surfaces with light-like axis in Minkowski 3-space. As a result, we classify helicoidal surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form on the surface.

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“…As a consequence, putting together with the results described above and theorems in [10], we have the following result: …”

Section: Equation (32) Can Be Written Asmentioning

confidence: 60%

“…In [8], Lee, Kim and Yoon studied ruled surfaces of the nondegenerate third fundamental form in Minkowski 3-space. Recently, Senoussi and Bekkar ( [10]) investigated helicoidal surfaces with non-lightlike axis in Minkowski 3-space satisfying the condition (1.2).…”

Section: Introductionmentioning

confidence: 99%

Helicoidal Surfaces of the Third Fundamental Form in Minkowski 3-Space

Choi¹,

Yoon²

2015

Bulletin of the Korean Mathematical Society

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“…Later Lopez [17] studied the hypersurfaces in R n+1 , Bekkar and Zoubir [18] classified the surfaces of revolution with non zero Gaussian curvature in the 3-dimensional Euclidean space E 3 and Lorentzian-Minkowski spaces and Bekkar and Senoussi [19] studied the factorable surfaces in the 3-dimensional Euclidean and Minkowski space under the condition (2.1). Also Difi et al [20] studied the translation-factorable surfaces in 3-dimensional Euclidean and Lorentzian spaces satisfying the condition ∆x i = λ i x i .…”

Section: Surfaces Satisfyingmentioning

confidence: 99%

Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$

BULCA SOKUR,

DİRİM

2023

Universal Journal of Mathematics and Applications

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In this paper, we study the conchodial surfaces in 3-dimensional Euclidean space with the condition $\Delta x_{i}=\lambda _{i}x_{i}$ where $\Delta $ denotes the Laplace operator with respect to the first fundamental form. We obtain the classification theorem for these surfaces satisfying under this condition. Furthermore, we have given some special cases for the classification theorem by giving the radius function $r(u,v)$ with respect to the parameters $u$ and $v$.

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“…Several results for the above question were obtained, when the ambient spaces are the Euclidean space ( [11]) and the Minkowski space ( [5,9,10,12,14,15].…”

Section: Introductionmentioning

confidence: 99%