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

##### MSC:
 53B25 Local submanifolds
##### Keywords:
surfaces; product manifold
Full Text:
##### References:
 [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 · Zbl 1125.53005 [4] Daniel B (2005) Isometric immersions into $${\mathbb S}^n\times{\mathbb R}$$ and $${\mathbb H}^n\times{\mathbb R}$$ and applications to minimal surfaces. to appear in Ann Glob Anal Geom
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