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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
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[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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