Geodesic
On the Gauss map of ruled surfaces
Glasgow mathematical journal, Tome 34 (1992) no. 3, pp. 355-359

Voir la notice de l'article provenant de la source Cambridge University Press

Let M2 be a (connected) surface in Euclidean 3-space E3, and let G:M2→S2(1) ⊂ E3 be its Gauss map. Then, according to a theorem of E. A. Ruh and J. Vilms [3], M2 is a surface of constant mean curvature if and only if, as a map from M2 to S2(1), G is harmonic, or equivalently, if and only ifwhere δ is the Laplace operator on M2 corresponding to the induced metric on M2 from E3 and where G is seen as a map from M2to E3. A special case of (1.1) is given byi.e., the case where the Gauss map G:M2→E3 is an eigenfunction of the Laplacian δ on M2. 
Baikoussis, Christos; Blair, David E. On the Gauss map of ruled surfaces. Glasgow mathematical journal, Tome 34 (1992) no. 3, pp. 355-359. doi: 10.1017/S0017089500008946
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[1] 1.Chen, B. Y., Dillen, F., Verstraelen, L. and Vrancken, L., Ruled surfaces of finite type, Bull. Austral. Math. Soc. 42 (1990), 447–453. Google Scholar | DOI

[2] 2.Dillen, F., Pas, J. and Verstraelen, L., On the Gauss map of surfaces of revolution, Bull. Inst. Math. Acad. Sinica, 18 (1990), 239–246. Google Scholar

[3] 3.Ruh, E. A. and Vilms, J., The tension field of the Gauss map, Trans. Amer. Math. Soc. 149 (1970), 569–573. Google Scholar | DOI

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