A. A. Agrachev and Y. L. Sachkov, Control theory from the geometric viewpoint, of Encyclopaedia of Mathematical Sciences Control Theory and Optimization, II, 2004.
DOI : 10.1007/978-3-662-06404-7

W. Ambrose and I. M. Singer, A theorem on holonomy, Transactions of the American Mathematical Society, vol.75, issue.3, pp.428-443, 1953.
DOI : 10.1090/S0002-9947-1953-0063739-1

F. Baudoin and M. Bonnefont, Curvature-dimension estimates for the Laplace???Beltrami operator of a totally geodesic foliation, Nonlinear Analysis: Theory, Methods & Applications, vol.126, pp.159-169, 2015.
DOI : 10.1016/j.na.2015.06.025
URL : https://hal.archives-ouvertes.fr/hal-01138611

F. Baudoin, M. Bonnefont, and N. Garofalo, A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincar?? inequality, Mathematische Annalen, vol.28, issue.1, pp.3-4833, 2014.
DOI : 10.1007/s00208-013-0961-y

F. Baudoin and N. Garofalo, Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries, Journal of the European Mathematical Society, vol.19, issue.1, pp.1101-3590, 2011.
DOI : 10.4171/JEMS/663

F. Baudoin, B. Kim, and J. Wang, Transverse Weitzenböck formulas and curvature dimension inequalities on Riemannian foliations with totally geodesic leaves. ArXiv e-prints, 0548.
DOI : 10.4310/cag.2016.v24.n5.a1
URL : http://arxiv.org/abs/1408.0548

A. Bella¨?chebella¨?che, The tangent space in sub-Riemannian geometry, Sub-Riemannian Geometry, Progress in Mathematics. Birkhäuser, 1996.

L. Bérard-bergery and J. Bourguignon, Laplacians and Riemannian submersions with totally geodesic fibres, Illinois J. Math, vol.26, issue.2, pp.181-200, 1982.

R. A. Blumenthal and J. J. Hebda, De Rham decomposition theorems for foliated manifolds, Annales de l???institut Fourier, vol.33, issue.2
DOI : 10.5802/aif.923

R. A. Blumenthal and J. J. Hebda, COMPLEMENTARY DISTRIBUTIONS WHICH PRESERVE THE LEAF GEOMETRY AND APPLICATIONS TO TOTALLY GEODESIC FOLIATIONS, The Quarterly Journal of Mathematics, vol.35, issue.4, pp.35383-392, 1984.
DOI : 10.1093/qmath/35.4.383

F. G. Brito, Une obstruction g??om??trique ?? l'existence de feuilletages de codimension 1 totalement g??od??siques, Journal of Differential Geometry, vol.16, issue.4, pp.675-684, 1981.
DOI : 10.4310/jdg/1214436371
URL : http://projecteuclid.org/download/pdf_1/euclid.jdg/1214436371

G. Cairns, Géométrie globale des feuilletages totalement géodésiques, C. R. Acad. Sci. Paris Sér. I Math, vol.297, issue.9, pp.525-527, 1983.

G. Cairns, A general description of totally geodesic foliations, Tohoku Mathematical Journal, vol.38, issue.1, pp.37-55, 1986.
DOI : 10.2748/tmj/1178228535

Y. Chitour, M. G. Molina, and P. Kokkonen, Symmetries of the rolling model, Mathematische Zeitschrift, vol.12, issue.2, pp.783-805, 2015.
DOI : 10.1007/s00209-015-1508-6
URL : https://hal.archives-ouvertes.fr/hal-01271285

Y. Chitour and P. Kokkonen, Rolling of Manifolds and Controllability in dimension three, Mémoires de la Société mathématique de France, vol.1, pp.1-118
DOI : 10.24033/msmf.455

D. Elworthy, Decompositions of diffusion operators and related couplings In Stochastic analysis and applications 2014, Math. Stat, vol.100, pp.283-306, 2014.

E. Falbel, C. Gorodski, and M. Rumin, Holonomy of Sub-Riemannian Manifolds, International Journal of Mathematics, vol.08, issue.03, pp.317-344, 1997.
DOI : 10.1142/S0129167X97000159

Z. Ge, Horizontal path spaces and Carnot-Carath??odory metrics, Pacific Journal of Mathematics, vol.161, issue.2, pp.255-286, 1993.
DOI : 10.2140/pjm.1993.161.255

K. A. Grasse and H. J. Sussmann, Global controllability by nice controls, In Nonlinear controllability and optimal control Monogr. Textbooks Pure Appl. Math, vol.133, pp.33-79, 1990.

E. Grong and A. Thalmaier, Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: part I, Math. Z, pp.10-1007, 2015.
DOI : 10.1007/s00209-015-1534-4
URL : http://arxiv.org/abs/1408.6873

E. Grong and A. Thalmaier, Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: part II, Mathematische Zeitschrift, vol.57, issue.2, 2015.
DOI : 10.1007/s00209-015-1535-3
URL : http://arxiv.org/abs/1408.6872

B. Hafassa, A. Mortada, Y. Chitour, and P. Kokkonen, Horizontal Holonomy for Affine Manifolds, Journal of Dynamical and Control Systems, vol.10, issue.3, pp.10-1007, 2015.
DOI : 10.1007/s10883-015-9274-7
URL : http://arxiv.org/abs/1411.0226

R. Hermann, A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle, Proc. Amer, pp.236-242, 1960.
DOI : 10.1090/S0002-9939-1960-0112151-4

F. Jean, Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning. SpringerBriefs in Mathematics, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01137580

T. H. Kang, H. K. Pak, and J. S. Pak, Laplacian on a totally geodesic foliation, Journal of Geometry, vol.255, issue.1-2, pp.74-79, 1997.
DOI : 10.1007/BF01252218

S. Kobayashi and K. Nomizu, Foundations of differential geometry, 1963.

I. Kolá?, P. W. Michor, and J. Slovák, Natural operations in differential geometry, 1993.
DOI : 10.1007/978-3-662-02950-3

R. Montgomery, Generic Distributions and Lie Algebras of Vector Fields, Journal of Differential Equations, vol.103, issue.2, pp.387-393, 1993.
DOI : 10.1006/jdeq.1993.1056

P. Nagy, Nearly K??hler geometry and Riemannian foliations, Asian Journal of Mathematics, vol.6, issue.3, pp.481-504, 2002.
DOI : 10.4310/AJM.2002.v6.n3.a5

H. Ozeki, Infinitesimal Holonomy Groups of Bundle Connections, Nagoya Mathematical Journal, vol.2, pp.105-123, 1956.
DOI : 10.1090/S0002-9947-1953-0063739-1

P. K. Rashevskii, On joining any two points of a completely nonholonomic space by an admissible line, Math. Ann, vol.3, pp.83-94, 1938.

B. L. Reinhart, Foliated Manifolds with Bundle-Like Metrics, The Annals of Mathematics, vol.69, issue.1, pp.119-132, 1959.
DOI : 10.2307/1970097

M. Rumin, Formes diff??rentielles sur les vari??t??s de contact, Journal of Differential Geometry, vol.39, issue.2, pp.281-330, 1994.
DOI : 10.4310/jdg/1214454873

A. V. Sarychev, Homotopy properties of the space of trajectories of a completely nonholonomic differential system, Dokl. Akad. Nauk SSSR, vol.314, issue.6, pp.1336-1340, 1990.

D. Sullivan, A foliation of geodesics is characterized by having no ???tangent homologies???, Journal of Pure and Applied Algebra, vol.13, issue.1, pp.101-104, 1978.
DOI : 10.1016/0022-4049(78)90046-4