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Loxodromes on helicoidal surfaces and tubes with variable radius in E⁴

Year 2019, , 1950 - 1958, 01.08.2019

Murat Babaarslan

https://doi.org/10.31801/cfsuasmas.455372
Cited By: 3

Abstract

In this paper, we
generalize the equations of loxodromes on helicoidal surfaces and canal
surfaces in E^3 to the case of 4-dimension (E^4). Also we give some examples via Mathematica.

Keywords

Loxodrome helicoidal surface tube with variable radius Euclidean 4-space

References

  • Bayram (Kılıç), B., Bulca, B., Kim, Y. H., Murathan, C., and Öztürk, G., Rotational embeddings in E⁴ with pointwise 1-type gauss map, Turk. J. Math., 35 (2011) 493--499.
  • Arslan, K., Bayram (Kılıç), B., Bulca, B., and Öztürk, G., Generalized Rotation Surfaces in E⁴, Results. Math., 61 (2012) 315--327.
  • Babaarslan, M., and Yayli, Y., Differential equation of the loxodrome on a helicoidal surface, Journal of Navigation, 68 (2015) 962--970.
  • Babaarslan, M., Loxodromes on Canal Surfaces in Euclidean 3-Space, Ann. Sofia Univ. Fac. Math and Inf., 103 (2016) 97--103.
  • Bulca, B., Arslan, K., Bayram, B., and Öztürk, G., Canal surfaces in 4-dimensional Euclidean space, Int. J. Optim. Control, Theor. Appl. (IJOCTA), 7 (2017) 83--89.
  • Dursun, U., and Turgay, N. C., General rotational surfaces in Euclidean space E⁴ with pointwise 1-type Gauss map, Math. Commun., 17 (2012) 71--81.
  • Erdoğdu, M., and Özdemir, M., Generating Four Dimensional Rotation Matrices, doi: 10.13140/RG.2.1.4118.3442, 2015.
  • Hieu D. T., and Thang, N. N., Bour's Theorem in 4-Dimensional Euclidean Space, Bull. Korean Math Soc., 54 (2017) 2081--2089.
  • Gal, R. O., and Pal, L., Some notes on drawing twofolds in 4-dimensional Euclidean space, Acta Univ. Sapientiae, Informatica, 1(2) (2009) 125--134.
  • Moore, C. L. E., Surfaces of Rotation in a Space of Four Dimensions, Ann. Math. (2), 21 (1919) 81--93.
  • Noble, C. A., Note on loxodromes, Bull. Am. Math. Soc., 1-2 (1905) 116--119.
  • Xu, Z., Feng, R., and Sun, J., Analytic and algebraic properties of canal surfaces, J. Comput. Appl. Math., 195 (2006) 220--228.
  • Yoon, D. W., Rotation Surfaces with Finite Type Gauss Map in E⁴, Indian J. Pure Appl. Math., 32 (2001) 1803--1808.
  • Yoon, D. W., Some Properties of the Clifford Torus as Rotational Surfaces, Indian J. Pure Appl. Math., 34 (2003) 907--915.

Year 2019, , 1950 - 1958, 01.08.2019

Murat Babaarslan

https://doi.org/10.31801/cfsuasmas.455372
Cited By: 3

Abstract

References

  • Bayram (Kılıç), B., Bulca, B., Kim, Y. H., Murathan, C., and Öztürk, G., Rotational embeddings in E⁴ with pointwise 1-type gauss map, Turk. J. Math., 35 (2011) 493--499.
  • Arslan, K., Bayram (Kılıç), B., Bulca, B., and Öztürk, G., Generalized Rotation Surfaces in E⁴, Results. Math., 61 (2012) 315--327.
  • Babaarslan, M., and Yayli, Y., Differential equation of the loxodrome on a helicoidal surface, Journal of Navigation, 68 (2015) 962--970.
  • Babaarslan, M., Loxodromes on Canal Surfaces in Euclidean 3-Space, Ann. Sofia Univ. Fac. Math and Inf., 103 (2016) 97--103.
  • Bulca, B., Arslan, K., Bayram, B., and Öztürk, G., Canal surfaces in 4-dimensional Euclidean space, Int. J. Optim. Control, Theor. Appl. (IJOCTA), 7 (2017) 83--89.
  • Dursun, U., and Turgay, N. C., General rotational surfaces in Euclidean space E⁴ with pointwise 1-type Gauss map, Math. Commun., 17 (2012) 71--81.
  • Erdoğdu, M., and Özdemir, M., Generating Four Dimensional Rotation Matrices, doi: 10.13140/RG.2.1.4118.3442, 2015.
  • Hieu D. T., and Thang, N. N., Bour's Theorem in 4-Dimensional Euclidean Space, Bull. Korean Math Soc., 54 (2017) 2081--2089.
  • Gal, R. O., and Pal, L., Some notes on drawing twofolds in 4-dimensional Euclidean space, Acta Univ. Sapientiae, Informatica, 1(2) (2009) 125--134.
  • Moore, C. L. E., Surfaces of Rotation in a Space of Four Dimensions, Ann. Math. (2), 21 (1919) 81--93.
  • Noble, C. A., Note on loxodromes, Bull. Am. Math. Soc., 1-2 (1905) 116--119.
  • Xu, Z., Feng, R., and Sun, J., Analytic and algebraic properties of canal surfaces, J. Comput. Appl. Math., 195 (2006) 220--228.
  • Yoon, D. W., Rotation Surfaces with Finite Type Gauss Map in E⁴, Indian J. Pure Appl. Math., 32 (2001) 1803--1808.
  • Yoon, D. W., Some Properties of the Clifford Torus as Rotational Surfaces, Indian J. Pure Appl. Math., 34 (2003) 907--915.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Murat Babaarslan 0000-0002-2770-4126

Publication Date August 1, 2019
Submission Date August 27, 2018
Acceptance Date April 18, 2019
Published in Issue Year 2019

Cite

APA Babaarslan, M. (2019). Loxodromes on helicoidal surfaces and tubes with variable radius in E⁴. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1950-1958. https://doi.org/10.31801/cfsuasmas.455372
AMA Babaarslan M. Loxodromes on helicoidal surfaces and tubes with variable radius in E⁴. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1950-1958. doi:10.31801/cfsuasmas.455372
Chicago Babaarslan, Murat. “Loxodromes on Helicoidal Surfaces and Tubes With Variable Radius in E⁴”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1950-58. https://doi.org/10.31801/cfsuasmas.455372.
EndNote Babaarslan M (August 1, 2019) Loxodromes on helicoidal surfaces and tubes with variable radius in E⁴. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1950–1958.
IEEE M. Babaarslan, “Loxodromes on helicoidal surfaces and tubes with variable radius in E⁴”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1950–1958, 2019, doi: 10.31801/cfsuasmas.455372.
ISNAD Babaarslan, Murat. “Loxodromes on Helicoidal Surfaces and Tubes With Variable Radius in E⁴”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1950-1958. https://doi.org/10.31801/cfsuasmas.455372.
JAMA Babaarslan M. Loxodromes on helicoidal surfaces and tubes with variable radius in E⁴. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1950–1958.
MLA Babaarslan, Murat. “Loxodromes on Helicoidal Surfaces and Tubes With Variable Radius in E⁴”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1950-8, doi:10.31801/cfsuasmas.455372.
Vancouver Babaarslan M. Loxodromes on helicoidal surfaces and tubes with variable radius in E⁴. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1950-8.

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