Magnetic flux ruled surfaces

Abstract

There is a unique curve called striction curve that is not present on a surface except a ruled surface. This curve is defined as the shortest distance with the help of a common perpendicular line between two adjacent rulings. In this work, we present Lorentz forces and magnetic striction curves produced by the geodesic Frenet frame {}ē,0.1emtruet¯,0.1emtrueg¯$$ \left\{\bar{e},\overline{t},\overline{g}\right\} $$ on the striction curve of the ruled surface defined by the spherical indicatrix curve in a magnetic field. We calculate magnetic vector fields of magnetic striction curves for truee‾,0.1emtruet¯$$ \overline{e},\overline{t} $$, and trueg¯$$ \overline{g} $$. Furthermore, we define magnetic flux surfaces constructed by magnetic vector fields along magnetic striction curves. We obtain developability conditions for these surfaces according to their curvature functions. Finally, we give some examples about magnetic flux surfaces.

A non-Newtonian magnetic curves in multiplicative Riemann manifolds

“…Bozkurt Z. et al conducted an investigation into N-magnetic curves and B-magnetic curves in 3D Riemann manifolds [29][30][31]. Magnetic curves have been a subject of study by researchers across various disciplines and within diverse spatial contexts [32][33][34][35][36][37].…”

Surface family interpolating a common spherical indicatrix curve

“…The study of curves and surfaces has wide application areas such as architectural design, computer aided design, astronomy, astrophysics and genetics [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. We encounter curves and surfaces in every differential geometry book.…”

“…al. [11] studied magnetic flux surfaces. Another interesting curve is the spherical indicatrix curve.…”