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Rectifying curves on a smooth surface immersed in the Euclidean space

Author

Listed:
  • Absos Ali Shaikh

    (University of Burdwan)

  • Pinaki Ranjan Ghosh

    (University of Burdwan)

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.

Suggested Citation

  • Absos Ali Shaikh & Pinaki Ranjan Ghosh, 2019. "Rectifying curves on a smooth surface immersed in the Euclidean space," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 883-890, December.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:4:d:10.1007_s13226-019-0361-4
    DOI: 10.1007/s13226-019-0361-4
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    Cited by:

    1. Absos Ali Shaikh & Pinaki Ranjan Ghosh, 2020. "Curves on a Smooth Surface with Position Vectors Lie in the Tangent Plane," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(3), pages 1097-1104, September.
    2. Absos Ali Shaikh & Pinaki Ranjan Ghosh, 2020. "Rectifying and Osculating Curves on a Smooth Surface," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 67-75, March.
    3. Absos Ali Shaikh & Mohamd Saleem Lone & Pinaki Ranjan Ghosh, 2020. "Normal Curves on a Smooth Immersed Surface," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1343-1355, December.

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