In this paper, we calculate the Gaussian curvatures of dual spherical indicatrix curves formed on unit sphere by Blaschke vectors and instantaneous Pfaff parallel equidistant ruled surfaces (DPERS) give relationships between these curvatures. addition to—in cases where base DPERS are closed—computing integral invariants curves. Additionally, show them. Finally, provide an example for each

In this paper we introduce generalized Darboux frame of a spacelike curve $\alpha$ lying on lightlike surface in Minkowski space $\mathbb{E}_{1}^{3}$. We prove that has two such frames and obtain frame's equations. find the relations between curvature functions $k_g$, $k_n$, $\tau_g$ with respect to its $\tilde{k}_{g}$, $\tilde{k}_{n}$, $\tilde{\tau}_{g}$ frames. show exist along straight line ...

The complete optical-gyration tensor for a monoclinic crystal of (2R, 3R)-(+)C4H6O6 has been determined by the tilter method at a wavelength of 680 nm. The tensor components in terms of rotatory power in relation to the principal axes of the indicatrix were found to be ρ◦ 11 = 79(7), ρ◦ 22 = 90(13), ρ◦ 33 = −70(4), ρ◦ 23 = −18(8)◦ mm−1 with ρ = −12.3(1.0)◦ mm−1 in the optic-axis directions. The...

We consider the curve straightening flow of inextensible, open, planar curves generated by the Kirchhoff bending energy. It can be considered as a model for the motion of elastic, inextensible rods in a high friction regime. We derive governing equations, namely a semilinear fourth order parabolic equation for the indicatrix and a second order elliptic equation for the Lagrange multiplier. We p...