O. Aharony, S. S. Gubser, J. Maldacena, H. Ooguri, and Y. Oz, Large N field theories, string theory and gravity, Physics Reports, vol.323, issue.3-4, pp.183-386, 2000.
DOI : 10.1016/S0370-1573(99)00083-6

M. T. Anderson, Topics in conformally compact Einstein metrics. Perspectives in Riemannian geometry, CRM Proc. Lecture Notes, pp.1-26, 2006.

A. Bagchi and R. Gopakumar, Galilean conformal algebras and AdS/CFT, Journal of High Energy Physics, vol.70, issue.07, p.37, 2009.
DOI : 10.1103/PhysRevD.56.4844

URL : http://arxiv.org/abs/0902.1385

K. Balasubramanian and J. Mcgreevy, Gravity Duals for Nonrelativistic Conformal Field Theories, Physical Review Letters, vol.101, issue.6, pp.61601-1101, 2008.
DOI : 10.1103/PhysRevLett.101.061601

E. Barletta and S. Dragomir, On the Curvature Groups of a CR Manifold, Mediterranean Journal of Mathematics, vol.3, issue.3-4, pp.399-407, 2006.
DOI : 10.1007/s00009-006-0086-6

X. Bekaert, E. Meunier, and S. Moroz, Symmetries and currents of the ideal and unitary Fermi gases, Journal of High Energy Physics, vol.660, issue.2
DOI : 10.1007/JHEP02(2012)113

URL : https://hal.archives-ouvertes.fr/hal-00667316

M. Blau, J. Hartong, and B. Rollier, Geometry of Schrödinger space-times, global coordinates, and harmonic trapping Geometry of Schrödinger space-times II: particles and fields probes of the causal structure, J. High Energy Phys. J. High Energy Phys, vol.7, issue.33, p.69, 2009.

G. Burdet, M. Perrin, and P. Sorba, About the non-relativistic structure of the conformal algebra, Communications in Mathematical Physics, vol.4, issue.2, pp.34-85, 1973.
DOI : 10.1007/BF01646438

G. Compère, S. De-buyl, S. Detournay, and K. Yoshida, Asymptotic symmetries of Schrödinger spacetimes, J. High Energy Phys, vol.10, issue.26, p.32, 2009.

S. Dragomir and G. Tomassini, Differential geometry and analysis on CR manifolds, Progress in Mathematics, vol.246, 2006.

C. Duval, Quelques procédures géométriques en dynamique des particules Nonrelativistic Conformal Symmetries and Bargmann Structures, Conformal Groups and Related Symmetries. Physical Results and Mathematical Background, 1982.

C. Duval, J. Elhadad, and G. M. Tuynman, The BRS method and geometric quantization: Some examples, Communications in Mathematical Physics, vol.28, issue.3, pp.535-557, 1990.
DOI : 10.1007/BF02125699

C. Duval, G. Burdet, H. P. Künzle, and M. Perrin, Bargmann structures and Newton-Cartan theory, Physical Review D, vol.31, issue.8, p.1841, 1985.
DOI : 10.1103/PhysRevD.31.1841

C. Duval, G. W. Gibbons, and P. A. Horváthy, Celestial mechanics, conformal structures, and gravitational waves, Physical Review D, vol.43, issue.12, p.3907, 1991.
DOI : 10.1103/PhysRevD.43.3907

C. Duval, M. Hassa¨?nehassa¨?ne, and P. A. Horváthy, The geometry of Schr??dinger symmetry in non-relativistic CFT, Annals of Physics, vol.324, issue.5, pp.1158-1167, 2009.
DOI : 10.1016/j.aop.2009.01.006

C. Duval and P. A. Horváthy, Non-relativistic conformal symmetries and Newton???Cartan structures, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.46, p.pp, 2009.
DOI : 10.1088/1751-8113/42/46/465206

URL : https://hal.archives-ouvertes.fr/hal-00373011

C. Duval and P. A. Horváthy, Conformal Galilei groups, Veronese curves and Newton???Hooke spacetimes, Journal of Physics A: Mathematical and Theoretical, vol.44, issue.33, p.pp, 2011.
DOI : 10.1088/1751-8113/44/33/335203

URL : https://hal.archives-ouvertes.fr/hal-00583704

C. Duval and V. Ovsienko, Conformally equivariant quantum Hamiltonians, Selecta Mathematica, vol.7, issue.3, pp.291-320, 2001.
DOI : 10.1007/PL00001403

M. Eastwood, Symmetries and Invariant Differential Pairings, Symmetry, Integrability and Geometry: Methods and Applications, vol.3, issue.10, 2007.
DOI : 10.3842/SIGMA.2007.113

J. Ehlers and W. Kundt, Exact solutions of the gravitational field equations " , in Gravitation: An introduction to current research, L. Witten Ed, 1962.

C. Fefferman, Monge-Ampere Equations, the Bergman Kernel, and Geometry of Pseudoconvex Domains, The Annals of Mathematics, vol.103, issue.3, pp.395-416, 1976.
DOI : 10.2307/1970945

C. Fefferman and C. R. Graham, Conformal invariants The ambient metric, The Mathematical Heritage of Elie Cartan Astérisque, hors série, pp.95-116, 1984.

C. Frances and E. Lyon, Géométrie et dynamique lorentziennes conformes, 2002.

G. W. Gibbons, Anti-de-Sitter Spacetime and Its Uses, Proceedings of the 2nd Samos Meeting on Cosmology, 2000.
DOI : 10.1007/3-540-46671-1_5

W. D. Goldberger, AdS/CFT duality for non-relativistic field theory, Journal of High Energy Physics, vol.2002, issue.03, p.69, 2009.
DOI : 10.1103/PhysRevLett.88.151301

C. R. Graham, On Sparling's Characterization of Fefferman Metrics, American Journal of Mathematics, vol.109, issue.5, pp.853-874, 1987.
DOI : 10.2307/2374491

V. Guillemin and S. Sternberg, Variations on a theme by Kepler, p.42, 1990.
DOI : 10.1090/coll/042

C. R. Hagen, Scale and Conformal Transformations in Galilean-Covariant Field Theory, Physical Review D, vol.5, issue.2, p.377, 1972.
DOI : 10.1103/PhysRevD.5.377

J. Hartong and B. Rollier, Asymptotically Schrödinger Space-Times: TsT Transformations and Thermodynamics, J. High Energy Phys, vol.29, pp.1-084, 2011.

M. Hassa¨?nehassa¨?ne and P. A. Horváthy, Field-Dependent Symmetries of a Non-relativistic Fluid Model, Annals of Physics, vol.282, issue.2, pp.218-246, 2000.
DOI : 10.1006/aphy.1999.6002

P. Ho?ava and C. M. Melby-thompson, Anisotropic conformal infinity, General Relativity and Gravitation, vol.03, issue.5, pp.1391-1400, 2011.
DOI : 10.1007/s10714-010-1117-y

R. Jackiw, Introducing scale symmetry, Physics Today, vol.25, issue.1, pp.23-27, 1972.
DOI : 10.1063/1.3070673

B. Julia and H. Nicolai, Null-Killing vector dimensional reduction and Galilean geometrodynamics, Nuclear Physics B, vol.439, issue.1-2, pp.291-323, 1995.
DOI : 10.1016/0550-3213(94)00584-2

URL : https://hal.archives-ouvertes.fr/hal-00004831

D. Kramer, H. Stephani, M. Maccallum, and E. Herlt, Solutions of the Gravitational Field equations, 1980.

H. P. Künzle, Galilei and Lorentz structures on space-time: Comparison of the corresponding geometry and physics, Ann. Inst. H. Poincaré. Phys. Théor, vol.17, pp.337-362, 1972.

J. M. Lee, The Fefferman metric and pseudo-Hermitian invariants, Transactions of the American Mathematical Society, vol.296, issue.1, pp.411-429, 1986.
DOI : 10.1090/S0002-9947-1986-0837820-2

T. Leistner and P. Nurowski, Ambient metrics of the n-dimensional ppwaves, Comm. Math. Phys, vol.296, pp.3-881, 2010.

F. Lin and S. Wu, Non-relativistic holography and singular black hole, Physics Letters B, vol.679, issue.1, pp.65-72, 2009.
DOI : 10.1016/j.physletb.2009.07.002

J. Maldacena, The large $N$ limit of superconformal field theories and supergravity, Advances in Theoretical and Mathematical Physics, vol.2, issue.2, pp.231-252, 1998.
DOI : 10.4310/ATMP.1998.v2.n2.a1

J. Maldacena, D. Martelli, and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry, Journal of High Energy Physics, vol.2008, issue.10, p.72, 2008.
DOI : 10.1088/1126-6708/2008/10/072

D. Minic and M. Pleimling, Correspondence between nonrelativistic anti-de Sitter space and conformal field theory, and aging-gravity duality, Physical Review E, vol.78, issue.6, p.61108, 2008.
DOI : 10.1103/PhysRevE.78.061108

U. Niederer, The maximal kinematical symmetry group of the free Schrödinger equation, Helv. Phys. Acta, vol.45, p.802, 1972.

R. Penrose, Conformal treatment of infinity " . 1964 Relativité, Groupes et Topologie (Lectures, Les Houches, pp.565-584, 1963.

M. Perrin, G. Burdet, and C. Duval, Chronoprojective invariance of the five-dimensional Schrodinger formalism, Classical and Quantum Gravity, vol.3, issue.3, pp.461-480, 1986.
DOI : 10.1088/0264-9381/3/3/020

C. Roger and J. Unterberger, The Schrödinger-Virasoro Algebra: Mathematical Structure and Dynamical Schrödinger Symmetries, Theoretical and Mathematical Physics Series, 2012.

M. Rooman and P. Spindel, geometry, Classical and Quantum Gravity, vol.18, issue.11, pp.2117-2124, 2001.
DOI : 10.1088/0264-9381/18/11/309

S. Schäfer-nameki, M. Yamazaki, and K. Yoshida, Coset construction for duals of non-relativistic CFTs, Journal of High Energy Physics, vol.2008, issue.05, pp.905-943, 2009.
DOI : 10.1016/S0550-3213(02)00003-2

D. T. Son, Toward an AdS/cold atoms correspondence: A geometric realization of the Schr??dinger symmetry, Physical Review D, vol.78, issue.4, p.46003, 2008.
DOI : 10.1103/PhysRevD.78.046003

J. Souriau, Géométrie globale duprobì emè a deux corps, Proc. IUTAM- ISIMM symposium on modern developments in analytical mechanics, 1982.