159 research outputs found
Helix surfaces in the special linear group
We characterize helix surfaces (constant angle surfaces) in the special
linear group . In particular, we give an explicit local
description of these surfaces in terms of a suitable curve and a 1-parameter
family of isometries of .Comment: Minor corrections. To appear in Annali di Matematica Pura e
Applicata. arXiv admin note: substantial text overlap with arXiv:1206.127
Helix surfaces in the Berger Sphere
We characterize helix surfaces in the Berger sphere, that is surfaces which
form a constant angle with the Hopf vector field. In particular, we show that,
locally, a helix surface is determined by a suitable 1-parameter family of
isometries of the Berger sphere and by a geodesic of a 2-torus in the
3-dimensional sphere.Comment: The main theorem has been modified and improved. Final version to
appear in Israel Journal of Mathematic
Constant angle surfaces in the Lorentzian Heisenberg group
In this paper, we define and, then, we characterize constant angle spacelike
and timelike surfaces in the three-dimensional Heisenberg group, equipped with
a 1-parameter family of Lorentzian metrics. In particular, we give an explicit
local parametrization of these surfaces and we produce some examples.Comment: 13 pages, 8 figure
Geodesics on an invariant surface
We study the geodesics on an invariant surface of a three dimensional
Riemannian manifold. The main results are: the characterization of geodesic
orbits; a Clairaut's relation and its geometric interpretation in some
remarkable three dimensional spaces; the local description of the geodesics;
the explicit description of geodesic curves on an invariant surface with
constant Gauss curvature.Comment: 14 pages, 1 figur
- …