OSCULATING-TYPE RULED SURFACES IN THE EUCLIDEAN 3-SPACE

Onur Kaya, Tanju Kahraman, Mehmet Önder

DOI Number
https://doi.org/10.22190/FUMI210220069K
First page
939
Last page
959

Abstract


In the present paper, a new type of ruled surfaces called osculating-type (OT)-ruled surface is introduced and studied. First, a new orthonormal frame is defined for OT-ruled surfaces. The Gaussian and the mean curvatures of these surfaces are obtained and the conditions for an OT-surface to be flat or minimal are given. Moreover, the Weingarten map of an OT-ruled surface is obtained and the normal curvature, the geodesic curvature and the geodesic torsion of any curve lying on surface are obtained. Finally, some examples related to helices and slant helices are introduced.

Keywords

osculating-type ruled surface, minimal surface, geodesic.

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References


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DOI: https://doi.org/10.22190/FUMI210220069K

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