# 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…

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Elliptic Weingarten surfaces: singularities, rotational examples and the halfspace theorem

- Mathematics
- 2022

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…

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