A New Approach to Rotational Weingarten Surfaces

@article{Carretero2022ANA,
  title={A New Approach to Rotational Weingarten Surfaces},
  author={Paula Carretero and Ildefonso Castro},
  journal={Mathematics},
  year={2022}
}
Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the notion of geometric linear momentum of a plane curve, we propose a new approach to the study of rotational Weingarten surfaces in Euclidean 3-space. Our contribution consists of reducing any type of Weingarten condition on a rotational surface to a first-order differential equation on the momentum of the… 
1 Citations
Elliptic Weingarten surfaces: singularities, rotational examples and the halfspace theorem
We show by phase space analysis that there are exactly 17 possible qualitative behaviors for a rotational surface in R that satisfies an arbitrary elliptic Weingarten equation W (κ1, κ2) = 0, and

References

SHOWING 1-10 OF 32 REFERENCES
Surfaces of revolution with prescribed mean curvature
In this paper we study a surface of revolution in the Euclidean three space Λ. The generating curve of the surface satisfies a nonlinear differential equation which describes the mean curvature. The
Hyperbolic Weingarten surfaces
  • B. van-BruntK. Grant
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1994
Abstract Weingarten surfaces which can be represented locally as solutions to second order hyperbolic partial differential equations are examined in this paper. In particular, the geometry of the
Classification of rotational surfaces in Euclidean space satisfying a linear relation between their principal curvatures
We classify all rotational surfaces in Euclidean space whose principal curvatures κ1 and κ2 satisfy the linear relation κ1=aκ2+b , where a and b are two constants. As a consequence of this
New Plane Curves with Curvature Depending on Distance from the Origin
Motivated by a problem posed by David A. Singer in 1999 and by the classical Bernoulli lemniscate and the Norwich spiral, we study the plane curves whose curvature is expressed in terms of the
Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers
Abstract This article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane 𝕃2
Rotational surfaces of constant astigmatism in space forms
Further Deformations of the Axially-Symmetric Non-Bending Surfaces
Abstract. We consider a special class of symmetrically loaded thin shells of revolution, which in the presence of certain disturbances of the equilibrium deform without bending. The whole family of
...
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