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Hypersurface families with Smarandache curves in Galilean 4-space

Year 2021, Volume: 70 Issue: 2, 744 - 761, 31.12.2021
https://doi.org/10.31801/cfsuasmas.794779

Abstract

In this paper, we study the hypersurface families with Smarandache curves in 4-dimensional Galilean space G4 and give the conditions for different Smarandache curves to be parameter and the curve which generates the Smarandache curves is geodesic on a hypersurface in G4. Also, we investigate three types of marching-scale functions for one of these hypersurfaces and construct an example for it.

References

  • Abdel-Baky, R.A., A surface family with a common asymptotic curve in the Euclidean 3-space, Asian Journal of Mathematics and Applications, Volume 2016, Article ID ama0363, 12 pages.
  • Altın, M., Yüzbasi, Z. K., Surfaces using Smarandache asymptotic curves in Galilean space, International Journal of Mathematical Combinatorics, 3 (2020), 1-15.
  • Bayram, E., Kasap, E., Hypersurface family with a common isogeodesic, "Vasile Alecsandri" University of Bacau Faculty of Sciences Scientific Studies and Research Series Mathematicsand Informatics, 24 (2) (2014), 5-24.
  • Bayram, E., Güler, F., Kasap, E., Parametric representation of a surface pencil with a common asymptotic curve, Computer-Aided Design, 44 (2012), 637-643, https://doi.org/10.1016/j.cad.2012.02.007.
  • Bayram, E., Kasap, E., Hypersurface family with a common isoasymptotic Curve, Hindawi publishing Corporation Geometry, Volume 2014, Article ID 623408, 6 pages, https://doi.org/10.1155/2014/623408.
  • Elzawy, M., Mosa, S., Smarandache curves in the Galilean 4-space G4, Journal of the Egyptian Mathematical Society, 25 (2017), 53-56, https://doi.org/10.1016/j.joems.2016.04.008.
  • Kasap, E., Akyildiz, F. T., Orbay, K., A generalization of surfaces family with common spatial geodesic, Applied Mathematics and Computation, 201 (2008), 781-789, https://doi.org/10.1016/j.amc.2008.01.016.
  • Kasap, E., Akyildiz, F. T., Surfaces with common geodesic in Minkowski 3-space, Appl. Math. Comput., 177 (2006), 260-270, https://doi.org/10.1016/j.amc.2005.11.005.
  • Yüzbası, Z. K., Bektas, M., On the construction of a surface family with common geodesic in Galilean space G3, De Gruyter Open Phys., 14 (2016), 360-363, DOI 10.1515/phys-2016-0041.
  • Yüzbası, Z. K., On a family of surfaces with common asymptotic curve in the Galilean space G3, Journal of Nonlinear Sci. Appl., 9 (2016), 518-523, DOI:10.22436/jnsa.009.02.17.
  • Yuzbası, Z. K., Yoon, D. W., An approach for hypersurface family with common geodesic curve in the 4D Galilean space G4, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 25 (4) (2018), 229-241, DOI:10.7468/jksmeb.2018.25.4.229.
  • Öztekin, H., Bozok, H. G., Inextensible ‡ows of curves in 4-dimensional Galilean space G4, Mathematical Sciences and Applications E-Notes, 1 (2) (2013), 28-34.
  • Saffak, G. and Kasap, E., Family of surface with a common null geodesic, Internat. J. Phys. Sci., 4 (8) (2009), 428-433.
  • Saffak Atalay, G., Kasap, E., Surfaces family with common Smarandache asymptotic curve, Bol. Soc. Paran. Mat., 34 (1) (2016), 9–20, doi:10.5269/bspm.v34i1.24392.
  • Wang, G. J., Tang, K., Tai, C. L., Parametric representation of a surface pencil with a common spatial geodesic, Computer-Aided Design, 36 (2004), 447-459, https://doi.org/10.1016/S0010-4485(03)00117-9.
  • Yılmaz, S., Consruction of the Frenet-Serret frame of a curve in 4D Galilean space and some applications, Int. Jour. of the Phys. Sci. Vol., 5 (8) (2010), 1284-1289.
  • Yoon, D. W., Lee, J. W., Lee, C. W., Osculating curves in the Galilean 4-space, International Journal of Pure and Applied Mathematics, 100 (4) (2015), 497-506, DOI:10.12732/IJPAM.V100I4.9.
Year 2021, Volume: 70 Issue: 2, 744 - 761, 31.12.2021
https://doi.org/10.31801/cfsuasmas.794779

Abstract

References

  • Abdel-Baky, R.A., A surface family with a common asymptotic curve in the Euclidean 3-space, Asian Journal of Mathematics and Applications, Volume 2016, Article ID ama0363, 12 pages.
  • Altın, M., Yüzbasi, Z. K., Surfaces using Smarandache asymptotic curves in Galilean space, International Journal of Mathematical Combinatorics, 3 (2020), 1-15.
  • Bayram, E., Kasap, E., Hypersurface family with a common isogeodesic, "Vasile Alecsandri" University of Bacau Faculty of Sciences Scientific Studies and Research Series Mathematicsand Informatics, 24 (2) (2014), 5-24.
  • Bayram, E., Güler, F., Kasap, E., Parametric representation of a surface pencil with a common asymptotic curve, Computer-Aided Design, 44 (2012), 637-643, https://doi.org/10.1016/j.cad.2012.02.007.
  • Bayram, E., Kasap, E., Hypersurface family with a common isoasymptotic Curve, Hindawi publishing Corporation Geometry, Volume 2014, Article ID 623408, 6 pages, https://doi.org/10.1155/2014/623408.
  • Elzawy, M., Mosa, S., Smarandache curves in the Galilean 4-space G4, Journal of the Egyptian Mathematical Society, 25 (2017), 53-56, https://doi.org/10.1016/j.joems.2016.04.008.
  • Kasap, E., Akyildiz, F. T., Orbay, K., A generalization of surfaces family with common spatial geodesic, Applied Mathematics and Computation, 201 (2008), 781-789, https://doi.org/10.1016/j.amc.2008.01.016.
  • Kasap, E., Akyildiz, F. T., Surfaces with common geodesic in Minkowski 3-space, Appl. Math. Comput., 177 (2006), 260-270, https://doi.org/10.1016/j.amc.2005.11.005.
  • Yüzbası, Z. K., Bektas, M., On the construction of a surface family with common geodesic in Galilean space G3, De Gruyter Open Phys., 14 (2016), 360-363, DOI 10.1515/phys-2016-0041.
  • Yüzbası, Z. K., On a family of surfaces with common asymptotic curve in the Galilean space G3, Journal of Nonlinear Sci. Appl., 9 (2016), 518-523, DOI:10.22436/jnsa.009.02.17.
  • Yuzbası, Z. K., Yoon, D. W., An approach for hypersurface family with common geodesic curve in the 4D Galilean space G4, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 25 (4) (2018), 229-241, DOI:10.7468/jksmeb.2018.25.4.229.
  • Öztekin, H., Bozok, H. G., Inextensible ‡ows of curves in 4-dimensional Galilean space G4, Mathematical Sciences and Applications E-Notes, 1 (2) (2013), 28-34.
  • Saffak, G. and Kasap, E., Family of surface with a common null geodesic, Internat. J. Phys. Sci., 4 (8) (2009), 428-433.
  • Saffak Atalay, G., Kasap, E., Surfaces family with common Smarandache asymptotic curve, Bol. Soc. Paran. Mat., 34 (1) (2016), 9–20, doi:10.5269/bspm.v34i1.24392.
  • Wang, G. J., Tang, K., Tai, C. L., Parametric representation of a surface pencil with a common spatial geodesic, Computer-Aided Design, 36 (2004), 447-459, https://doi.org/10.1016/S0010-4485(03)00117-9.
  • Yılmaz, S., Consruction of the Frenet-Serret frame of a curve in 4D Galilean space and some applications, Int. Jour. of the Phys. Sci. Vol., 5 (8) (2010), 1284-1289.
  • Yoon, D. W., Lee, J. W., Lee, C. W., Osculating curves in the Galilean 4-space, International Journal of Pure and Applied Mathematics, 100 (4) (2015), 497-506, DOI:10.12732/IJPAM.V100I4.9.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Mustafa Altın 0000-0001-5544-5910

Ahmet Kazan 0000-0002-1959-6102

Hacı Bayram Karadağ 0000-0001-6474-877X

Publication Date December 31, 2021
Submission Date September 14, 2020
Acceptance Date March 8, 2021
Published in Issue Year 2021 Volume: 70 Issue: 2

Cite

APA Altın, M., Kazan, A., & Karadağ, H. B. (2021). Hypersurface families with Smarandache curves in Galilean 4-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 744-761. https://doi.org/10.31801/cfsuasmas.794779
AMA Altın M, Kazan A, Karadağ HB. Hypersurface families with Smarandache curves in Galilean 4-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2021;70(2):744-761. doi:10.31801/cfsuasmas.794779
Chicago Altın, Mustafa, Ahmet Kazan, and Hacı Bayram Karadağ. “Hypersurface Families With Smarandache Curves in Galilean 4-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 2 (December 2021): 744-61. https://doi.org/10.31801/cfsuasmas.794779.
EndNote Altın M, Kazan A, Karadağ HB (December 1, 2021) Hypersurface families with Smarandache curves in Galilean 4-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 744–761.
IEEE M. Altın, A. Kazan, and H. B. Karadağ, “Hypersurface families with Smarandache curves in Galilean 4-space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 2, pp. 744–761, 2021, doi: 10.31801/cfsuasmas.794779.
ISNAD Altın, Mustafa et al. “Hypersurface Families With Smarandache Curves in Galilean 4-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (December 2021), 744-761. https://doi.org/10.31801/cfsuasmas.794779.
JAMA Altın M, Kazan A, Karadağ HB. Hypersurface families with Smarandache curves in Galilean 4-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:744–761.
MLA Altın, Mustafa et al. “Hypersurface Families With Smarandache Curves in Galilean 4-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 2, 2021, pp. 744-61, doi:10.31801/cfsuasmas.794779.
Vancouver Altın M, Kazan A, Karadağ HB. Hypersurface families with Smarandache curves in Galilean 4-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):744-61.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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