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Loxodromes on helicoidal surfaces and tubes with variable radius in E⁴

Year 2019, Volume: 68 Issue: 2, 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, Volume: 68 Issue: 2, 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 Volume: 68 Issue: 2

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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