Classification of rotational special Weingarten surfaces of minimal type in S^2 x R and H^2 x R

TL;DR

This paper completes the classification of rotational special Weingarten surfaces of minimal type in the product spaces S^2 x R and H^2 x R, characterized by a specific relation between mean and extrinsic curvature.

Contribution

It provides a complete classification of these surfaces, extending previous work by analyzing the relation h=f(h^2-K_e) under certain curvature constraints.

Findings

Classification of all such surfaces in S^2 x R and H^2 x R

Identification of conditions for existence and uniqueness

Extension of known results in minimal surface theory

Abstract

In this paper we finish the classification of rotational special Weingarten surfaces in S^2 x R and H^2 x R; i.e. rotational surfaces in S^2 x R and H^2 x R whose mean curvature h and extrinsic curvature K_e satisfy h=f(h^2-K_e), for some function f in C^1([0,+infty)) such that 4x(f'(x))^2<1 for any x>=0.