On conformally flat Lorentz parabolic manifolds

• Autorzy: Yoshinobu Kamishima
• Języki publikacji: EN

Abstrakty

EN

We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type.

Słowa kluczowe

EN

Lorentz parabolic structure; Conformally flat Lorentz structure; Fefferman-Lorentz manifold; Uniformization; Holonomy group; Developing map; Similarity structure

Kategorie tematyczne

• 57S25: Groups acting on specific manifolds
• 53A30: Conformal differential geometry
• 53C50: Lorentz manifolds, manifolds with indefinite metrics
• 57S30: Discontinuous groups of transformations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 6
• Strony: 861-878

Daty

wydano

2014-06-01

online

2014-03-19

Twórcy

autor

Yoshinobu Kamishima

• Tokyo Metropolitan University

Bibliografia

• [1] Aristide T., Closed similarity Lorentzian affine manifolds, Proc. Amer. Math. Soc., 2004, 132(12), 3697–3702 http://dx.doi.org/10.1090/S0002-9939-04-07560-4
• [2] Barbot T., Charette V., Drumm T., Goldman W.M., Melnick K., A primer on the (2+1) Einstein universe, In: Recent Developments in Pseudo-Riemannian Geometry, ESI Lect. Math. Phys., European Mathematical Society, Zürich, 2008, 179–229 http://dx.doi.org/10.4171/051-1/6
• [3] Chen S.S., Greenberg L., Hyperbolic Spaces, Contribution to Analysis, Academic Press, New York, 1974, 49–87
• [4] Fefferman C., Parabolic invariant theory in complex analysis, Adv. in Math., 1979, 31(2), 131–262 http://dx.doi.org/10.1016/0001-8708(79)90025-2
• [5] Goldman W.M., Kamishima Y., The fundamental group of a compact flat Lorentz space form is virtually polycyclic, J. Differential Geom., 1984, 19(1), 233–240
• [6] Kamishima Y., Conformally flat manifolds whose development maps are not surjective. I, Trans. Amer. Math. Soc., 1986, 294(2), 607–623 http://dx.doi.org/10.1090/S0002-9947-1986-0825725-2
• [7] Kamishima Y., Geometric flows on compact manifolds and global rigidity, Topology, 1996, 35(2), 439–450 http://dx.doi.org/10.1016/0040-9383(95)00025-9
• [8] Kamishima Y., Lorentzian similarity manifold, Cent. Eur. J. Math., 2012, 10(5), 1771–1788 http://dx.doi.org/10.2478/s11533-012-0076-9
• [9] Kamishima Y., Fefferman-Lorentz manifolds arising from parabolic geometry (manuscript)
• [10] Kamishima Y., Tsuboi T., CR-structures on Seifert manifolds, Invent. Math., 1991, 104(1), 149–163 http://dx.doi.org/10.1007/BF01245069
• [11] Kobayashi S., Transformation Groups in Differential Geometry, Ergeb. Math. Grenzgeb., 70, Springer, New York-Heidelberg, 1972 http://dx.doi.org/10.1007/978-3-642-61981-6
• [12] Kulkarni R.S., On the principle of uniformization, J. Differential Geom., 1978, 13(1), 109–138
• [13] Kulkarni R.S., Conformal structures and Möbius structures, Aspects Math., E12, Conformal Geometry, Vieweg, Braunschweig, 1988, 1–39
• [14] Kulkarni R.S., Pinkall U., Uniformizations of geometric structures with applications to conformall geometry, In: Differential Geomtery, Peñiscola, June 2–9, 1985, Lecture Notes in Math., 1209, Springer, Berlin, 1986, 190–209 http://dx.doi.org/10.1007/BFb0076632
• [15] Lee J.M., The Fefferman metric and pseudo-Hermitian invariants, Trans. Amer. Math. Soc., 1986, 296(1), 411–429
• [16] Lee K.B., Raymond F., Seifert Fiberings, Math. Surveys Monogr., 166, American Mathematical Society, Providence, 2010 http://dx.doi.org/10.1090/surv/166
• [17] Miner R.R., Spherical CR manifolds with amenable holonomy, Internat. J. Math., 1990, 1(4), 479–501 http://dx.doi.org/10.1142/S0129167X9000023X
• [18] Schoen R., On the conformal and CR automorphism groups, Geom. Funct. Anal., 1995, 5(2), 464–481 http://dx.doi.org/10.1007/BF01895676
• [19] Sternberg S., Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, 1964

Identyfikatory

DOI

10.2478/s11533-013-0379-5