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Frenet Curves in Euclidean 4-Space

Year 2017, Volume: 10 Issue: 2, 56 - 66, 29.10.2017
https://doi.org/10.36890/iejg.545050

Abstract


References

  • [1] Appell, P., Trait´e de M´ecanique Rationnelle, Vol. 1, 6th ed., Gauthier-Villars, Paris, 1941.
  • [2] Cambie, S., Goemans, W. and Bussche, V., Rectifying curves in n-dimensional Euclidean space. Turk. J. Math., 40 (2016), 2010-2023.
  • [3] Chen, B.-Y., When does the position vector of a space curve always lie in its rectifying plane? Amer. Math. Monthly, 110 (2003), 147-152.
  • [4] Chen, B.-Y. and Dillen, F., Rectifying curves as centrodes and extremal curves. Bull. Inst. Math. Academia Sinica, 33 (2005), 77-90.
  • [5] Chen, B.-Y., Geometry of position functions of Riemannian submanifolds in pseudo-Euclidean space. J. Geom., 74 (2002),: 61-77.
  • [6] Deshmukh, S., Chen, B.-Y. and Shammari, S., On Rectifying curves in Euclidean 3-space (to appear in Turkish J. Math.).
  • [7] Deshmukh, S., Chen, B.-Y. and Turki, N. B., Two differential equations for Frenet curves in Euclidean 3-space and their applications. (submitted for publication).
  • [8] Gertzbei, S., Seligman, J., Holtby, R., Chan, K., Ogston, N., Kapasouri, A., Tile, M. and Cruickshank B., Centrode patterns and segmental instability in degenerative disk disease. Spine,10 (1985), 257-261.
  • [9] Ilarslan, K. and Nesovic, E., Some characterizations of rectifying curves in the Euclidean space E4. Turk. J. Math., 32 (2008), 21-30.
  • [10] Kim, C. Y., Park, J. H. and Yorozu, S., Curves On the unit 3-Sphere S3(1) in Euclidean 4-Space R4. Bull Korean Math. Soc., 50 2013;: 1599-1622.
  • [11] Kuhnel, W., Differential geometry: curves-surfaces-manifolds. Braunschweig: Wiesbaden, 1999.
  • [12] Mikes J. Differential geometry of special mappings. Palacky Univ. Press, Olomouc, 2015.
  • [13] Monterde, J., Curves with constant curvature ratios. Bull. Mexican Math. Soc., 13 (2007), 177-186.
  • [14] Ogston, N., King, G., Gertzbein, S., Tile, M., Kapasouri, A. and Rubenstein, J., Centrode patterns in the lumbar spine-base-line studies in normal subjects. Spine, 11 (1986), 591-595.
  • [15] Romero-Fuster, M. C. and Sanabria-Codesal, E., Generalized helices,twistings and flattenings of curves in n-space. Matematica Contemporanea, 17 (1999), 267-280.
  • [16] Weiler, P.J. and Bogoch, R. E., Kinematics of the distal radioulnar joint in rheumatoid-arthritis-an in-vivo study using centrode analysis. J. Hand Surgery, 20A (1995), 937-943.
  • [17] Yeh, H. and Abrams, J.I., Principles of Mechanics of Solids and Fluids. Vol. 1, McGraw-Hall, New York, 1960.
Year 2017, Volume: 10 Issue: 2, 56 - 66, 29.10.2017
https://doi.org/10.36890/iejg.545050

Abstract

References

  • [1] Appell, P., Trait´e de M´ecanique Rationnelle, Vol. 1, 6th ed., Gauthier-Villars, Paris, 1941.
  • [2] Cambie, S., Goemans, W. and Bussche, V., Rectifying curves in n-dimensional Euclidean space. Turk. J. Math., 40 (2016), 2010-2023.
  • [3] Chen, B.-Y., When does the position vector of a space curve always lie in its rectifying plane? Amer. Math. Monthly, 110 (2003), 147-152.
  • [4] Chen, B.-Y. and Dillen, F., Rectifying curves as centrodes and extremal curves. Bull. Inst. Math. Academia Sinica, 33 (2005), 77-90.
  • [5] Chen, B.-Y., Geometry of position functions of Riemannian submanifolds in pseudo-Euclidean space. J. Geom., 74 (2002),: 61-77.
  • [6] Deshmukh, S., Chen, B.-Y. and Shammari, S., On Rectifying curves in Euclidean 3-space (to appear in Turkish J. Math.).
  • [7] Deshmukh, S., Chen, B.-Y. and Turki, N. B., Two differential equations for Frenet curves in Euclidean 3-space and their applications. (submitted for publication).
  • [8] Gertzbei, S., Seligman, J., Holtby, R., Chan, K., Ogston, N., Kapasouri, A., Tile, M. and Cruickshank B., Centrode patterns and segmental instability in degenerative disk disease. Spine,10 (1985), 257-261.
  • [9] Ilarslan, K. and Nesovic, E., Some characterizations of rectifying curves in the Euclidean space E4. Turk. J. Math., 32 (2008), 21-30.
  • [10] Kim, C. Y., Park, J. H. and Yorozu, S., Curves On the unit 3-Sphere S3(1) in Euclidean 4-Space R4. Bull Korean Math. Soc., 50 2013;: 1599-1622.
  • [11] Kuhnel, W., Differential geometry: curves-surfaces-manifolds. Braunschweig: Wiesbaden, 1999.
  • [12] Mikes J. Differential geometry of special mappings. Palacky Univ. Press, Olomouc, 2015.
  • [13] Monterde, J., Curves with constant curvature ratios. Bull. Mexican Math. Soc., 13 (2007), 177-186.
  • [14] Ogston, N., King, G., Gertzbein, S., Tile, M., Kapasouri, A. and Rubenstein, J., Centrode patterns in the lumbar spine-base-line studies in normal subjects. Spine, 11 (1986), 591-595.
  • [15] Romero-Fuster, M. C. and Sanabria-Codesal, E., Generalized helices,twistings and flattenings of curves in n-space. Matematica Contemporanea, 17 (1999), 267-280.
  • [16] Weiler, P.J. and Bogoch, R. E., Kinematics of the distal radioulnar joint in rheumatoid-arthritis-an in-vivo study using centrode analysis. J. Hand Surgery, 20A (1995), 937-943.
  • [17] Yeh, H. and Abrams, J.I., Principles of Mechanics of Solids and Fluids. Vol. 1, McGraw-Hall, New York, 1960.
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Sharief Deshmukh

İbrahim Al-dayel This is me

Kazım İlarslan

Publication Date October 29, 2017
Published in Issue Year 2017 Volume: 10 Issue: 2

Cite

APA Deshmukh, S., Al-dayel, İ., & İlarslan, K. (2017). Frenet Curves in Euclidean 4-Space. International Electronic Journal of Geometry, 10(2), 56-66. https://doi.org/10.36890/iejg.545050
AMA Deshmukh S, Al-dayel İ, İlarslan K. Frenet Curves in Euclidean 4-Space. Int. Electron. J. Geom. October 2017;10(2):56-66. doi:10.36890/iejg.545050
Chicago Deshmukh, Sharief, İbrahim Al-dayel, and Kazım İlarslan. “Frenet Curves in Euclidean 4-Space”. International Electronic Journal of Geometry 10, no. 2 (October 2017): 56-66. https://doi.org/10.36890/iejg.545050.
EndNote Deshmukh S, Al-dayel İ, İlarslan K (October 1, 2017) Frenet Curves in Euclidean 4-Space. International Electronic Journal of Geometry 10 2 56–66.
IEEE S. Deshmukh, İ. Al-dayel, and K. İlarslan, “Frenet Curves in Euclidean 4-Space”, Int. Electron. J. Geom., vol. 10, no. 2, pp. 56–66, 2017, doi: 10.36890/iejg.545050.
ISNAD Deshmukh, Sharief et al. “Frenet Curves in Euclidean 4-Space”. International Electronic Journal of Geometry 10/2 (October 2017), 56-66. https://doi.org/10.36890/iejg.545050.
JAMA Deshmukh S, Al-dayel İ, İlarslan K. Frenet Curves in Euclidean 4-Space. Int. Electron. J. Geom. 2017;10:56–66.
MLA Deshmukh, Sharief et al. “Frenet Curves in Euclidean 4-Space”. International Electronic Journal of Geometry, vol. 10, no. 2, 2017, pp. 56-66, doi:10.36890/iejg.545050.
Vancouver Deshmukh S, Al-dayel İ, İlarslan K. Frenet Curves in Euclidean 4-Space. Int. Electron. J. Geom. 2017;10(2):56-6.

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