Chains, null-chains, and CR geometry
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- by Lisa K. Koch PDF
- Trans. Amer. Math. Soc. 338 (1993), 245-261 Request permission
Abstract:
A system of distinguished curves distinct from chains is defined on indefinite nondegenerate ${\text {CR}}$ hypersurfaces; the new curves are called null-chains. The properties of these curves are explored, and it is shown that two sufficiently nearby points of any nondegenerate ${\text {CR}}$ hypersurface can be connected by either a chain or a null-chain.References
- Robert L. Bryant, Holomorphic curves in Lorentzian CR-manifolds, Trans. Amer. Math. Soc. 272 (1982), no. 1, 203–221. MR 656486, DOI 10.1090/S0002-9947-1982-0656486-4
- D. Burns Jr., K. Diederich, and S. Shnider, Distinguished curves in pseudoconvex boundaries, Duke Math. J. 44 (1977), no. 2, 407–431. MR 445009
- D. Burns Jr. and S. Shnider, Real hypersurfaces in complex manifolds, Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 2, Williams Coll., Williamstown, Mass., 1975) Amer. Math. Soc., Providence, R.I., 1977, pp. 141–168. MR 0450603 É. Cartan, Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes. I, Œuvres Complètes, Gauthier-Villars, Paris, 1955, pp. 1231-1304; II, Œuvres Complètes, Gauthier-Villars, Paris, 1955, pp. 1217-1238. J.-H. Cheng, Chain-preserving differomorphisms and $CR$ equivalence, preprint.
- S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. MR 425155, DOI 10.1007/BF02392146
- Frank A. Farris, An intrinsic construction of Fefferman’s CR metric, Pacific J. Math. 123 (1986), no. 1, 33–45. MR 834136
- Charles L. Fefferman, Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains, Ann. of Math. (2) 103 (1976), no. 2, 395–416. MR 407320, DOI 10.2307/1970945
- C. Robin Graham, On Sparling’s characterization of Fefferman metrics, Amer. J. Math. 109 (1987), no. 5, 853–874. MR 910354, DOI 10.2307/2374491
- Steven G. Harris, A triangle comparison theorem for Lorentz manifolds, Indiana Univ. Math. J. 31 (1982), no. 3, 289–308. MR 652817, DOI 10.1512/iumj.1982.31.31026
- Howard Jacobowitz, Chains in CR geometry, J. Differential Geom. 21 (1985), no. 2, 163–194. MR 816668
- Lisa K. Koch, Chains on CR manifolds and Lorentz geometry, Trans. Amer. Math. Soc. 307 (1988), no. 2, 827–841. MR 940230, DOI 10.1090/S0002-9947-1988-0940230-2
- N. G. Kruzhilin, Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces, Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985), no. 3, 566–591, 672 (Russian). MR 794956
- Demir N. Kupeli, Degenerate submanifolds in semi-Riemannian geometry, Geom. Dedicata 24 (1987), no. 3, 337–361. MR 914829, DOI 10.1007/BF00181606
- John M. Lee, The Fefferman metric and pseudo-Hermitian invariants, Trans. Amer. Math. Soc. 296 (1986), no. 1, 411–429. MR 837820, DOI 10.1090/S0002-9947-1986-0837820-2 H. Poincaré, Les fonctions analytiques de deux variables et la représentation conforme, Rend. Circ. Mat. Palermo (1907), 185. G. Sparling, Twistor theory and the characterization of Fefferman’s conformal structures, preprint.
- S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geometry 13 (1978), no. 1, 25–41. MR 520599
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 338 (1993), 245-261
- MSC: Primary 32F40; Secondary 53C56
- DOI: https://doi.org/10.1090/S0002-9947-1993-1100695-4
- MathSciNet review: 1100695