Geodesic
Immersed surfaces and pencils of planes in 3-space
Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 133-136

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

Let M be a compact connected boundaryless surface and f: M → R3 a smooth immersion transverse to a straight line L. Thus there is an even number p of points xεM such that f(x)εL. Under further transversality assumptions on f (see §3) there is a finite number q of points x of M such that the plane containing f(x) and L touches f(M) at f(x). These assumptions are mild in the sense that they hold for any f in an open dense subset of the space of smooth immersions under consideration. Suppose that the Gaussian curvature of f(M) is positive at q+ of these points and negative at q−, with q = q++ q−. Thenwhere e(M) denotes the Euler number of M. 
Carvalho, F. J.Craveiro de. Immersed surfaces and pencils of planes in 3-space. Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 133-136. doi: 10.1017/S0017089500004560
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