Rotational Linear Weingarten Surfaces into the Euclidean Sphere

TL;DR

This paper provides a comprehensive classification of all rotational linear Weingarten surfaces within the Euclidean sphere, characterized by a linear relation between mean and Gaussian curvatures.

Contribution

It offers a complete description of these surfaces, extending the understanding of curvature relations in spherical geometry.

Findings

Classification of all rotational linear Weingarten surfaces in S3.

Explicit descriptions based on the linear relation aH + bK = c.

New insights into curvature relations in spherical geometry.

Abstract

The aim of this paper is to present a complete description of all rotational linear Weingarten surface into the Euclidean sphere S3. These surfaces are characterized by a linear relation aH+bK=c, where H and K stand for their mean and Gaussian curvatures, respectively, whereas a; b and c are real constants.