4 papers
Catenaries and singular minimal surfaces in the simply isotropic space
Luiz C. B. da Silva, Rafael López
This paper investigates the hanging chain problem in the simply isotropic plane as well as its 2-dimensional analog in the simply isotropic space. The simply isotropic plane and sp…
Differential geometry of invariant surfaces in simply isotropic and pseudo-isotropic spaces
Luiz C. B. da Silva
We study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, the simply and pseudo isotropic geometries are the study o…
Characterization of manifolds of constant curvature by spherical curves
Luiz C. B. da Silva, José D. da Silva
It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical…
Differential Geometry of Rotation Minimizing Frames, Spherical Curves, and Quantum Mechanics of a Constrained Particle
Luiz C. B. da Silva
This thesis is devoted to the Differential Geometry of curves and surfaces along with applications in Quantum Mechanics. In the 1st part we introduce the well known Frenet frame. L…