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Curves on a Smooth Surface with Position Vectors Lie in the Tangent Plane

Author

Listed:
  • Absos Ali Shaikh

    (The University of Burdwan)

  • Pinaki Ranjan Ghosh

    (The University of Burdwan)

Abstract

The present paper deals with a study of curves on a smooth surface whose position vector always lies in the tangent plane of the surface and it is proved that such curves remain invariant under isometry of surfaces. It is also shown that length of the position vector, tangential component of the position vector and geodesic curvature of a curve on a surface whose position vector always lies in the tangent plane are invariant under isometry of surfaces.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:3:d:10.1007_s13226-020-0452-2
    DOI: 10.1007/s13226-020-0452-2
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    References listed on IDEAS

    as
    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.
    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.
    Full references (including those not matched with items on IDEAS)

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    1. 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.
    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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