6 papers · 1 filter
Classification of invariant Gauss curvature solitons in the Heisenberg space $\nil$
Rafael Belli, Rafael López
In this paper, we classify all solitons of the Gauss curvature flow in the three-dimensional Heisenberg group that are invariant under a one-parameter group of amb…
Curvatures of curves in endowed with a canonical linear connection
Muhittin Evren Aydın, Rafael López
We investigate the geometry of plane curves in endowed with a canonical linear connection. By introducing the notions of the tangential and geodesic curvatures, we p…
Generalization of Newton's minimal resistance problem to Riemannian surfaces
Rafael López
We extend Newton's problem of minimal resistance to Riemannian surfaces endowed with a geodesic coordinate system, which includes the two-dimensional space forms such as the sphere…
Gauss curvature solitons on invariant surfaces in the homogeneous space Sol
Rafael Belli, Rafael López
We classify invariant surfaces in the 3-dimensional solvable Lie group $\sol$ that act as solitons for the Gauss curvature flow. We consider solitons associated with the canonical…
A note on helices in the Euclidean space and in the hyperbolic space
Rafael López
We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyp…
Stability of vertical and radial graphs in the Euclidean space with density
Rafael López
It is proved that vertical graphs and radial graphs are strongly stable for a certain type of densities in Euclidean space . Particular cases of these densities…