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In this paper, by taking a Frenet curve lying on a parametric or implicit hypersurface and using the extended Darboux frame field of this curve, we give a new method… Click to show full abstract
In this paper, by taking a Frenet curve lying on a parametric or implicit hypersurface and using the extended Darboux frame field of this curve, we give a new method for calculating the shape operator’s matrix of the hypersurface depending on the extended Darboux frame curvatures. This new method enables us to obtain the Gaussian and mean curvatures of the hypersurface depending on the geodesic torsions of the curve and the normal curvatures of the hypersurface.
Keywords:
hypersurface;
new method;
shape operator
Journal Title: Filomat
Year Published: 2018
Link to full text (if available)
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Journal Title: Filomat
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!