40 citations · 105 across the 16 of their papers we have counts for
17 papers
Curves and surfaces making a constant angle with a parallel transported direction in Riemannian spaces
Luiz C. B. da Silva, Gilson S. Ferreira, José D. da Silva
In the last two decades, much effort has been dedicated to studying curves and surfaces according to their angle with a given direction. However, most findings were obtained using…
Catenaries in Riemannian Surfaces
Luiz C. B. da Silva, Rafael López
The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author [López, arXiv:2208.13694]. In this work, we define catenaries on any…
Catenaries and minimal surfaces of revolution in hyperbolic space
Luiz C. B. da Silva, Rafael López
We introduce the concept of extrinsic catenary in the hyperbolic plane. Working in the hyperboloid model, we define an extrinsic catenary as the shape of a curve hanging under its…
Compatible director fields in
Luiz C. B. da Silva, Tal Bar, Efi Efrati
The geometry and interactions between the constituents of a liquid crystal, which are responsible for inducing the partial order in the fluid, may locally favor an attempted phase…
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…
Characterization of manifolds of constant curvature by ruled surfaces
Luiz C. B. da Silva, José D. da Silva
We investigate ruled surfaces in 3d Riemannian manifolds, i.e., surfaces foliated by geodesics. In 3d space forms, we find the striction curve, distribution parameter, and the firs…
Curves orthogonal to a vector field in Euclidean spaces
Luiz C. B. da Silva, Gilson S. Ferreira
A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any…
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…
Surfaces of revolution with prescribed mean and skew curvatures in Lorentz-Minkowski space
Luiz C. B. da Silva
In this work, we investigate the problem of finding surfaces in the Lorentz-Minkowski 3-space with prescribed skew () and mean () curvatures, which are defined through the di…
The geometry of Gauss map and shape operator in simply isotropic and pseudo-isotropic spaces
Luiz C. B. da Silva
In this work, we are interested in the differential geometry of surfaces in simply isotropic and pseudo-isotropic spaces, which consists…
Characterization of curves that lie on a geodesic sphere or on a totally geodesic hypersurface in a hyperbolic space or in a sphere
Luiz C. B. da Silva, José Deibsom da Silva
The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equatio…
Rotation minimizing frames and spherical curves in simply isotropic and pseudo-isotropic 3-spaces
Luiz C. B. da Silva
In this work, we are interested in the differential geometry of curves in the simply isotropic and pseudo-isotropic 3-spaces, which are examples of Cayley-Klein geometries whose ab…
Characterization of Spherical and Plane Curves Using Rotation Minimizing Frames
Luiz C. B. da Silva
In this work, we study plane and spherical curves in Euclidean and Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By conveniently writing the curvature an…
Moving frames and the characterization of curves that lie on a surface
Luiz C. B. da Silva
In this work we are interested in the characterization of curves that belong to a given surface. To the best of our knowledge, there is no known general solution to this problem. I…
Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential
L. C. B. da Silva, C. C. Bastos, F. G. Ribeiro
The experimental techniques have evolved to a stage where various examples of nanostructures with non-trivial shapes have been synthesized, turning the dynamics of a constrained pa…