New developments on constant angle property in $${\mathbb {S}}^2\times {\mathbb {R}}$$ S 2 × R

Abstract

In the present paper, we classify curves and surfaces in \({\mathbb {S}}^2\times \mathbb {R}\), which make constant angle with a rotational Killing vector field. We obtain the explicit parametrizations of such curves and surfaces, and we find examples in some particular cases. Finally, we give the complete classification of minimal constant angle surfaces in \({\mathbb {S}}^2\times \mathbb {R}\).