A New Method for Finding the Shape Operator of a Hypersurface in Euclidean 4-Space
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DOI: 10.2298/fil1817827u
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… read more here.
Keywords: hypersurface; new method; shape operator;
Quaternionic Shape Operator and Rotation Matrix on Ruled Surfaces
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DOI: 10.3390/axioms12050486
Abstract: In this article, we examine the relationship between Darboux frames along parameter curves and the Darboux frame of the base curve of the ruled surface. We derive the equations of the quaternionic shape operators, which… read more here.
Keywords: rotation matrix; operator rotation; quaternionic shape; shape operator ... See more keywords