Constant Angle Surfaces in $\mathbb{S}^3(1) \times \mathbb{R}$

TL;DR

This paper classifies constant angle surfaces in the product space ^3(1)   with parallel mean curvature vectors, expanding understanding of their geometric properties.

Contribution

It provides a complete classification of constant angle surfaces in ^3(1)   with parallel mean curvature vectors, a novel result in differential geometry.

Findings

Classification of constant angle surfaces with parallel mean curvature vector

Explicit descriptions of such surfaces in ^3(1)  

New insights into the geometry of surfaces in product spaces

Abstract

In this article we study surfaces in $\mathbb{S}^3(1) \times \mathbb{R}$ for which the $\mathbb{R}$-direction makes a constant angle with the normal plane. We give a complete classification for such surfaces with parallel mean curvature vector.