Abstract
The main objective of the present paper is to investigate a sufficient condition for which a rectifying curve on a smooth surface remains invariant under isometry of surfaces, and also it is shown that under such an isometry the component of the position vector of a rectifying curve on a smooth surface along the normal to the surface is invariant.
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References
A. Pressley, Elementary differential geometry, Springer-Verlag, (2001).
M. P. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Inc, New Jersey, (1976).
B.-Y. Chen, What does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly, 110 (2003), 147–152.
B.-Y. Chen and F. Dillen, Rectifying curve as centrode and extremal curve, Bull. Inst. Math. Acad. Sinica, 33(2) (2005), 77–90.
S. Deshmukh, B.-Y. Chen, and S. H. Alshammari, On a rectifying curves in Euclidean 3-space, Turk. J. Math., 42 (2018), 609–620.
Acknowledgement
We are immensely grateful to Professor Dr. Bang-Yen Chen, Michigan State University, for his valuable comments. The second author greatly acknowledges to The University Grants Commission, Government of India for the award of Junior Research Fellow.
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Shaikh, A.A., Ghosh, P.R. Rectifying curves on a smooth surface immersed in the Euclidean space. Indian J Pure Appl Math 50, 883–890 (2019). https://doi.org/10.1007/s13226-019-0361-4
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DOI: https://doi.org/10.1007/s13226-019-0361-4