Some characterizations of rectifying and osculating curves on a smooth immersed surface

초록

The present paper deals with some characterizations of rectifying and osculating curves on a smooth surface with respect to the reference frame {(T) over right arrow, (N) over right arrow, (T) over right arrow x (N) over right arrow}. We have computed the components of position vectors of rectifying and osculating curves along (T) over right arrow, (N) over right arrow, (T) over right arrow x (N) over right arrow($) over right arrow Nand then investigated their invariancy under isometry of surfaces, and it is shown that they are invariant iff either the normal curvature of the curve is invariant or the position vector of the curve is in the direction of the tangent vector to the curve. (C) 2021 Elsevier B.V. All rights reserved.

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