Differential Geometry of Rectifying Submanifolds

Year 2016, Volume: 9 Issue: 2, 1 - 8, 30.10.2016

Bang-yen Chen

https://doi.org/10.36890/iejg.584566

Cited By: 9

Abstract

Keywords

Rectifying curve, rectifying submanifold

References

• [1] Cambie, S., Goemans, W. and Van den Bussche, I., Rectifying curves in the n-dimensional Euclidean space. Turkish J. Math. 40 (2016), no.1, 210–223.
• [2] Chen, B.-Y., Geometry of Submanifolds. Marcel Dekker, New York, 1973.
• [3] Chen, B.-Y., Constant-ratio hypersurfaces. Soochow J. Math. 21 (2001), 353–361.
• [4] Chen, B.-Y., Geometry of position functions of Riemannian submanifolds in pseudo-Euclidean space. J. Geom. 74 (2002), 61–77.
• [5] Chen, B.-Y., Convolution of Riemannian manifolds and its applications. Bull. Austral. Math. Soc. 66 (2002), no. 2, 177–191.
• [6] Chen, B.-Y., When does the position vector of a space curve always lie in its rectifying plane?. Amer. Math. Monthly 110 (2003), no. 2, 147–152.
• [7] Chen, B.-Y., More on convolution of Riemannian manifolds. Beiträge Algebra Geom. 44 (2003), 9–24.
• [8] Chen, B.-Y., Constant-ratio space-like submanifolds in pseudo-Euclidean space. Houston J. Math. 29 (2003), no. 2, 281–294
• [9] Chen, B.-Y., Pseudo-Riemannian geometry, δ-invariants and applications. World Scientific, 2011.
• [10] Chen, B.-Y., Topics in differential geometry associated with position vector fields on Euclidean submanifolds. Arab J. Math. Sci. 23 (2017), no. 1 (Special Issue on Geometry and Global Analysis), doi:10.1016/j.ajmsc.2016.08.001.
• [11] Chen, B.-Y. and Dillen, F., Rectifying curves as centrodes and extremal curves. Bull. Inst. Math. Acad. Sinica 33 (2005), no. 2, 77–90.
• [12] Gungor, M. A. and Tosun, M., Some characterizations of quaternionic rectifying curves. Differ. Geom. Dyn. Syst. 13 (2011), 89–100.
• [13] S. Hiepko, Eine innere Kennzeichnung der verzerrten Produkte, Math. Ann. 241 (1979), no. 3, 209–215.
• [14] Ilarslan, K., Nesovic, E. and Petrovic-Torgasev, M., Some characterizations of rectifying curves in the Minkowski 3-space. Novi Sad J. Math. 33 (2003), no. 2, 23–32.
• [15] Ilarslan, K. and Nesovic, E., On rectifying curves as centrodes and extremal curves in the Minkowski 3-space. Novi Sad J. Math. 37 (2007), no. 1, 53–64.
• [16] Ilarslan, K. and Nesovic, E., Some characterizations of rectifying curves in the Euclidean space E4. Turkish J. Math. 32 (2008), no. 1, 21–30.
• [17] Ilarslan, K. and Nesovic, E., Some relations between normal and rectifying curves in Minkowski space-time. Int. Electron. J. Geom. 7 (2014), no. 1, 26–35.
• [18] Lucas, P. and Ortega-Yagues, J. A., Rectifying curves in the three-dimensional sphere. J. Math. Anal. Appl. 421 (2015), no. 2, 1855–1868.
• [19] Ozbey, and Oral, M., A study on rectifying curves in the dual Lorentzian space. Bull. Korean Math. Soc. 46 (2009), no. 5, 967–978.
• [20] Yilmaz, B., Gok, I. and Yayli, Y., Extended rectifying curves in Minkowski 3-space. Adv. Appl. Clifford Algebr. 26 (2016), no. 2, 861–872.
• [21] Yücesan, A., Ayyildiz, N. and Coken, A. C., On rectifying dual space curves. Rev. Mat. Complut. 20 (2007), no. 2, 497–506.