Dillen, Franki; Fastenakels, Johan; Van der Veken, Joeri; Vrancken, Luc Constant angle surfaces in \({\mathbb S}^2\times {\mathbb R}\). (English) Zbl 1140.53006 Monatsh. Math. 152, No. 2, 89-96 (2007). 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. Reviewer: Constantin Călin (Iaşi) Cited in 1 ReviewCited in 55 Documents MSC: 53B25 Local submanifolds Keywords:surfaces; product manifold PDFBibTeX XMLCite \textit{F. Dillen} et al., Monatsh. Math. 152, No. 2, 89--96 (2007; Zbl 1140.53006) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.