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Zbl 1140.53006
Dillen, Franki; Fastenakels, Johan; Van der Veken, Joeri; Vrancken, Luc
Constant angle surfaces in ${\Bbb S}^2\times {\Bbb R}$. (English)
[J] Monatsh. Math. 152, No. 2, 89-96 (2007). ISSN 0026-9255; ISSN 1436-5081/e

The authors prove that if $M$ is a surfaces immersed in $\Bbb S^2\times\Bbb R$, then $M$ is a constant angle surface if and only if the immersion $F: M\rightarrow\Bbb S^2\times\Bbb R:(u,v) \Rightarrow F(u,v),$ 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 $\Bbb S^2$ and $\theta\in [0,\pi]$ is the constant angle.
[Constantin Călin (Iaşi)]

MSC 2000:: *53B25 Local submanifolds

Keywords: surfaces; product manifold

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