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

Absos Ali Shaikh () and Pinaki Ranjan Ghosh ()
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Absos Ali Shaikh: The University of Burdwan
Pinaki Ranjan Ghosh: The University of Burdwan

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 3, 1097-1104

Abstract: 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.

Keywords: Isometry of surfaces; first fundamental form; second fundamental form; geodesic curvature; 53A04; 53A05; 53A15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0452-2

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