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Constant angle surfaces in $\Bbb H^{2} \times \Bbb R$. (English) Zbl 1173.53012
Let $H^2 \times\Bbb R$ be the Riemannian product of a two-dimensional real hyperbolic plane with constant sectional curvature $-1$ and a Euclidean line. The authors classify all surfaces in $H^2 \times\Bbb R$ for which the angle between the normal spaces of the surface and the Euclidean line $\Bbb R$ in the product is constant.

53B25Local submanifolds
Full Text: DOI arXiv
[1] P. Cermelli and A.J. Di Scala. Constant-angle surfaces in liquid crystals. Philosophical Magazine, 87(12) (2007), 1871--1888. · doi:10.1080/14786430601110364
[2] F. Dillen, J. Fastenakels, J. Van der Veken and L. Vrancken. Constant Angle Surfaces in S 2 {$\times$} $\mathbb{R}$. Monaths. Math., 152(2) (2007), 89--96. · Zbl 1140.53006 · doi:10.1007/s00605-007-0461-9
[3] F. Dillen and M.I. Munteanu. Surfaces in $\mathbb{H}$ 2 {$\times$} $\mathbb{R}$. Pure and Applied Differential Geometry, PADGE 2007, Berichte aus der Mathematik (Shaker Verlag) Eds. Franki Dillen, Ignace Van de Woestyne, 185--193. · Zbl 1144.53068
[4] J. Fastenakels, M.I. Munteanu and J. Van der Veken. Constant angle surfaces in the Heisenberg group, preprint. · Zbl 1218.53019
[5] M.I. Munteanu and A.I. Nistor. A new approach on constant angle surface in E 3, to appear in Turkish J. Math., (2009). · Zbl 1175.53006
[6] P. Petersen. Riemannian Geometry. Graduate Texts in Mathematics, Springer Verlag, (1997). · Zbl 0898.53035
[7] J.G. Ratcliffe. Foundations of Hyperbolic Manifolds. 2-nd Edition, Graduate Texts in Mathematics, Springer (2006). · Zbl 1106.51009