Rectifying and Osculating Curves on a Smooth Surface

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

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 67-75

Abstract: 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.

Keywords: Rectifying curve; osculating curve; isometry of surfaces; first fundamental form; second fundamental form; geodesic curvature; normal curvature; 53A04; 53A05; 53A15 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13226-020-0385-9

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