Frenet Curves in Euclidean 4-Space

Year 2017, , 56 - 66, 29.10.2017

Sharief Deshmukh , İbrahim Al-dayel Kazım İlarslan

https://doi.org/10.36890/iejg.545050

Cited By: 1

Abstract

Keywords

Frenet curves, rectifying curves, Chen curves, ccr-curves, curvatures

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.