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Constant angle surfaces in ${𝕊}^{2}×ℝ$. (English) Zbl 1140.53006
The authors prove that if $M$ is a surfaces immersed in ${𝕊}^{2}×ℝ$, then $M$ is a constant angle surface if and only if the immersion $F:M\to {𝕊}^{2}×ℝ:\left(u,v\right)⇒F\left(u,v\right),$ where $F\left(u,v\right)=\left(cos\left(ucos\theta \right)f\left(v\right)+sin\left(ucos\theta \right)f\left(v\right)×{f}^{\text{'}}\left(v\right),sin\theta \right),$ $f:I\to {S}^{2}$ is a unit speed curve in ${𝕊}^{2}$ and $\theta \in \left[0,\pi \right]$ is the constant angle.

##### MSC:
 53B25 Local submanifolds
##### Keywords:
surfaces; product manifold
##### References:
 [1] · Zbl 1078.53053 · doi:10.1007/BF02392562 [2] Albujer AL, Alías LJ (2005) On Calabi-Bernstein results for maximal surfaces in Lorentzian products. Preprint [3] Alías LJ, Dajczer M, Ripoll J (2007) A Bernstein-type theorem for Riemannian manifolds with a Killing field. Preprint [4] Daniel B (2005) Isometric immersions into ${𝕊}^{n}×ℝ$ and ${ℍ}^{n}×ℝ$ and applications to minimal surfaces. to appear in Ann Glob Anal Geom [5] [6]