Geodesic
Transversally affine foliations
Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 106-111

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

Let F be a smooth foliation of codimension p on a smooth manifold Mm. We can define F by an atlas of coordinate charts (U, (x, y)), called leaf charts, where (x, y): U → Rm−p × Rp are coordinate functions for which the leaves of F are given by y1 constant,...,yp constant, in U. Clearly, on the overlap of two such leaf charts (U, (x, y)) and (U′, (x′, y′)) we have a coordinate transformation of the formIf y′ is always affine in y, i.e.where and Bi are constants, we shall say that F is a transversally affine foliation. This notion is, in a sense, dual to that of affine foliation, see [2], in which x′ is affine in x and each leaf has an induced flat affine structure. 
Furness, P. M. D.; Fédida, E. Transversally affine foliations. Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 106-111. doi: 10.1017/S0017089500002810
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