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Rectifying and Osculating Curves on a Smooth Surface

Author

Listed:
  • Absos Ali Shaikh

    (University of Burdwan)

  • Pinaki Ranjan Ghosh

    (University of Burdwan)

Abstract

The main motive of the paper is to look on rectifying and osculating curves on a smooth surface. In this paper we find the normal and geodesic curvature for a rectifying curve on a smooth surface and we also prove that geodesic curvature is invariant under the isometry of surfaces such that rectifying curves remain. We find a sufficient condition for which an osculating curve on a smooth surface remains invariant under isometry of surfaces and also we prove that the component of the position vector of an osculating curve α(s) on a smooth surface along any tangent vector to the surface at α(s) is invariant under such isometry.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:1:d:10.1007_s13226-020-0385-9
    DOI: 10.1007/s13226-020-0385-9
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    References listed on IDEAS

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    1. 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.
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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.

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    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 & 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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