Geodesic
Timelike hypersurfaces in anti-de Sitter space from a~contact viewpoint
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 219-234.

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We study timelike hypersurfaces in anti-de Sitter space from the viewpoint of the Lagrangian/ Legendrian singularity theory. 
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L. Chen; S. Izumiya; D. Pei. Timelike hypersurfaces in anti-de Sitter space from a~contact viewpoint. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 219-234. https://geodesic-test.mathdoc.fr/item/CMFD_2011_42_a21/

[1] Aledo J. A., Espinar J. M., “A conformal representation for linear Weingarten surfaces in the de Sitter space”, J. Geom. Phys., 57 (2007), 1669–1677 | DOI | MR | Zbl

[2] Arnol'd V. I., Gusein-Zade S. M., Varchenko A. N., Singularities of differentiable maps, v. I, Birkhäuser, Basel, 1986

[3] Bröcker Th., Differential germs and catastrophes, Cambridge University Press, Cambridge–New York, 1975 | MR

[4] Chen L., “Singularities of timelike Anti de Sitter Gauss images”, Hokkaido Mathematical Journal, 38 (2009), 701–720 | MR | Zbl

[5] Chen L., Izumiya S., “A mandala of Legendrian dualities for pseudo-spheres in semi-Euclidean space”, Proc. Japan Acad., Ser. A, 85 (2009), 49–54 | DOI | MR | Zbl

[6] Chen L., Izumiya S., “Singularities of Anti de Sitter torus Gauss maps”, Bull. Braz. Math. Soc. (to appear)

[7] Fujimori S., Saji K., Umehara M., Yamada K., “Singularities of maximal surfaces”, Math. Z., 259:4 (2008), 827–848 | DOI | MR | Zbl

[8] Goryunov V. V., “Projections of generic surfaces with boundaries”, Adv. Soviet Math., 1, 1990, 157–200 | MR | Zbl

[9] Izumiya S., “Timelike hypersurfaces in de Sitter space and Legendrian singularities”, Journal of Mathematical Sciences, 144:1 (2007), 3789–3803 | DOI | MR | Zbl

[10] Izumiya S., “Legendrian dualities and spacelike hypersurfaces in the lightcone”, Moscow Mathematical Journal, 9:2 (2009), 325–357 | MR | Zbl

[11] Izumiya S., Pei D.-H., Sano T., “Singularities of hyperbolic Gauss maps”, Proc. London Math. Soc., 3:86 (2003), 485–512 | DOI | MR | Zbl

[12] Izumiya S., Romero Fuster M. C., “The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space”, Selecta Mathematica (NS), 13 (2007), 23–55 | DOI | MR | Zbl

[13] Izumiya S., Takahashi M., “Spacelike parallels and evolutes in Minkowski pseudo-spheres”, J. Geometry and Physics, 57 (2007), 1569–1600 | DOI | MR | Zbl

[14] Kasedou M., “Singularities of lightcone Gauss images of spacelike hypersurfaces in de Sitter space”, Journal of Geometry, 94 (2009), 107–121 | DOI | MR | Zbl

[15] Maldacena M., “The large $N$ limit of superconformal field theories and supergravity”, Adv. Theor. Math. Phys., 2 (1998), 231–252 | MR | Zbl

[16] Martinet J., Singularities of smooth functions and maps, Cambridge Univ. Press, Cambridge, 1982 | MR | Zbl

[17] Mather J., “Stability of $C^\infty$ mappings III: Finitely determined map germs”, Publ. Math. I. H. E. S., 35 (1968), 127–156 | Zbl

[18] Montaldi J. A., “On contact between submanifolds”, Michigan Math. J., 33 (1986), 81–85 | MR

[19] Montaldi J. A., “On generic composites of maps”, Bull. London Math. Soc., 23 (1991), 81–85 | DOI | MR | Zbl

[20] O'Neil B., Semi-Riemannian geometry, Academic Press, New York, 1983 | MR

[21] Randall L., Sundrum R., “An alternative to compactification”, Physical Review Letters, 83 (1999), 4690–4693 | DOI | MR | Zbl

[22] Witten E., “Anti de Sitter space and holography”, Adv. Theor. Math. Phys., 2 (1998), 253–291 | MR | Zbl

[23] Zakalyukin V. M., “Lagrangian and legendrian singularities”, Funct. Anal. Appl., 10:1 (1976), 23–31 | DOI | MR | Zbl

[24] Zakalyukin V. M., “Reconstructions of fronts and caustics depending one parameter and versality of mappings”, J. Sov. Math., 27 (1984), 2713–2735 | DOI | Zbl