M. İ. MUNTEANU, Marian Ioan Munteanu, Ana–Irina Nistor

A New Approach on Constant Angle Surfaces in E3

In this paper we study constant angle surfaces in Euclidean 3--space. Even that the result is a consequence of some classical results involving the Gauss map (of the surface), we give another approach to classify all surfaces for which the unit normal makes a constant angle with a fixed direction.

Anahtar Kelimeler:

Constant angle surfaces, Euclidean space

A New Approach on Constant Angle Surfaces in E3

Keywords:

Constant angle surfaces, Euclidean space,

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[1] Cermelli, P. and Di Scala, A. J.: Constant-angle surfaces in liquid crystals, Philosophical Magazine, 87 (12), 1871 - 1888 (2007).
[2] Dillen, F. and Fastenakels, J. and Van der Veken, J. and Vrancken, L.: Constant Angle Surfaces in 2×, Monaths. Math. 152 (2), 89–96 (2007).
[3] Dillen, F. and Munteanu, M.I.: Constant Angle Surfaces in 2 ×, arXiv:0705.3744v1 [math.DG] (2007) to appear in Bull. Braz. Math. Soc., (2009).
[4] Dillen, F. and Munteanu, M.I.: Surfaces in + ×, Proc. of the conference Pure and Applied Differential Geometry, PADGE, Brussels 2007, (Eds. F. Dillen and I. van de Woestyne), 185 - 193 (2007).
[5] Howard, R.: The geometry of shadow boundaries on surfaces in space, preprint. 177
[6] Meeks, W. and Rosenberg, H.: Stable minimal surfaces in 2 ×, J. Differential Geometry, 68 (3), 515-534 (2004).
[7] Prinsen, P. and van der Schoot, P.: Shape and director-field transformations of tactoids, Phys. Rev. E, 68, 021701.1- 021701.11 (2003).
[8] Prinsen, P. and van der Schoot, P.: Continuous director-field transformations of nematic tactoids, Eur. Phys. J. E, 13, 35-41 (2004).
[9] Prinsen, P. and van der Schoot, P.: Parity breaking in nematic tactoids, J. Phys. Cond. Matter, 16, 8835-8850 (2004).
[10] Rosenberg, H.: Minimal surfaces in 2 × , Illinois J. Math., 46 (4), 1177-1195 (2002).
[11] Virga, E.G.: Drops of nematic liquid crystals, Arch. Rat. Mech. Anal., 107, 371-390 (1989).