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Null Helices in Lorentzian Space Forms
In this paper we introduce a reference along a null curve in an n-dimensional Lorentzian space with the minimum number of curvatures. That reference generalizes the reference of Bonnor for nullExpand
Surfaces in the 3-dimensional Lorentz-Minkowski space satisfying Δx = Ax + B
In this paper we locally classify the surfaces M s 2 in the 3-dimensional Lorentz-Minkowski space L 3 verifying the equation Δx = Ax + B, where A is an endomorphism of L 3 and B is a constant vector.Expand
General Helices in the Three-Dimensional Lorentzian Space Forms
We present some Lancret-type theorems for general helices in the three-dimensional Lorentzian space forms which show remarkable differences with regard to the same question in Riemannian space forms.Expand
On a certain class of conformally flat Euclidean hypersurfaces
Let x : Mp−−→IRn+1 be an isometric immersion of a manifold Mp into the Euclidean space IR and ∆ its Laplacian. The family of such immersions satisfying the condition ∆x = λx, λ ∈ IR, is characterizedExpand
Particles with curvature and torsion in three-dimensional pseudo-Riemannian space forms
We consider the motion of relativistic particles described by an action which is a function of the curvature and torsion of the particle path. The Euler–Lagrange equations and the dynamical constantsExpand
Null finite type hypersurfaces in space forms
In [5], Chen gives a classification of null 2-type surfaces in the Euclidean 3-space and he shows in [6] that a similar characterization cannot be given for a surface in the Euclidean 4-space. InExpand
A conformal variational approach for helices in nature
We propose a two step variational principle to describe helical structures in nature. The first one is governed by an energy action which is a linear function in both curvature and torsion allowingExpand
Geometrical particle models on 3D null curves
Abstract The simplest (2+1)-dimensional mechanical systems associated with light-like curves, already studied by Nersessian and Ramos, are reconsidered. The action is linear in the curvature of theExpand
Some Variational Problems on Curves and Applications
Some variational problems are revisited showing elastic curves as a key tool to find solutions to some classical problems such as Willmore surfaces, Willmore-Chen submanifolds and 2-dimensionalExpand