On the dual Darboux rotation axis of the timelike dual space curve.
Differential-geometrical conditions between geodesic curves and ruled surfaces in the Lorentz space.
Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection
We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riemannian manifold and of its a non-degenerate hypersurface with respect to a semi-symmetric metric connection....
Relaxed hyperelastic curves
We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space E³, and we derive the intrinsic equations for a relaxed hyperelastic curve on a surface. Then, by examining relaxed hyperelastic curves in a plane, on a sphere and on a cylinder, we show that geodesics are relaxed hyperelastic curves in a plane and on a sphere. But on a cylinder, they are relaxed hyperelastic curves only in special cases.
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