The Burns-Epstein invariant and deformation of CR structures
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Duke Mathematical Journal

The Burns-Epstein invariant and deformation of CR structures

Jih-Hsin Cheng and John M. Lee

Source: Duke Math. J. Volume 60, Number 1 (1990), 221-254.

First Page PDF: View first page of article (PDF, 112 KB)

Primary Subjects: 32F40
Secondary Subjects: 32G07, 58E11

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077297146
Mathematical Reviews number (MathSciNet): MR1047122
Zentralblatt MATH identifier: 0704.53028
Digital Object Identifier: doi:10.1215/S0012-7094-90-06008-9

References

[A] T. Aubin, Best constants in the Sobolev imbedding theorem: the Yamabe problem, Sem. on Differential Geometry ed. S.-T. Yau, Ann. Math. Studies, vol. 102, Princeton University Press, Princeton, 1982, pp. 173–184.
Mathematical Reviews (MathSciNet): MR84d:58078
Zentralblatt MATH: 0483.53041
[BE1] D. Burns and C. Epstein, A global invariant for three dimensional CR-manifolds, Invent. Math. 92 (1988), no. 2, 333–348.
Mathematical Reviews (MathSciNet): MR89b:53060
Zentralblatt MATH: 0643.32006
Digital Object Identifier: doi:10.1007/BF01404456
[BE2] D. Burns and C. Epstein, Characteristic numbers of bounded domains, preprint.
[BS] D. Burns and S. Shnider, Spherical hypersurfaces in complex manifolds, Invent. Math. 33 (1976), no. 3, 223–246.
Mathematical Reviews (MathSciNet): MR54:7875
Zentralblatt MATH: 0357.32012
Digital Object Identifier: doi:10.1007/BF01404204
[C]1 E. Cartan, Sur la géometrie pseudo-conforme des hypersurfaces de l' espace de deux variables complexe, I, Ann. Mat. 11 (1932), 17–90.
Zentralblatt MATH: 0005.37304
Digital Object Identifier: doi:10.1007/BF02417822
[C]2 E. Cartan, Sur la géometrie pseudo-conforme des hypersurfaces de l' espace de deux variables complexe, II, Ann. Sc. Norm. Sup. Pisa 1 (1932), 333–354.
Zentralblatt MATH: 0005.37401
[Ch] J.-H. Cheng, On the curvature of CR-structures and its covariant derivatives, Math. Z. 196 (1987), no. 2, 203–209.
Mathematical Reviews (MathSciNet): MR89b:32023
Zentralblatt MATH: 0613.32012
Digital Object Identifier: doi:10.1007/BF01163655
[CM]1 S.-S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271, Erratum, Acta Math. 150 (1983) 297.
Mathematical Reviews (MathSciNet): MR54:13112
Zentralblatt MATH: 0302.32015
Digital Object Identifier: doi:10.1007/BF02392146
[CM]2 S. S. Chern and J. K. Moser, Erratum: “Real hypersurfaces in complex manifolds”, Acta Math. 150 (1983), no. 3-4, 297.
Mathematical Reviews (MathSciNet): MR85a:32014
Digital Object Identifier: doi:10.1007/BF02392974
[D1] D. DeTurck, Deforming metrics in the direction of their Ricci tensors, J. Differential Geom. 18 (1983), no. 1, 157–162.
Mathematical Reviews (MathSciNet): MR85j:53050
Zentralblatt MATH: 0517.53044
Project Euclid: euclid.jdg/1214509286
[D2] D. DeTurck, Deforming metrics in the direction of their Ricci tensors: IMPROVED, preprint.
Mathematical Reviews (MathSciNet): MR697987
Project Euclid: euclid.jdg/1214509286
[FS] G. B. Folland and E. M. Stein, Estimates for the $\bar \partial \sb{b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429–522.
Mathematical Reviews (MathSciNet): MR51:3719
Zentralblatt MATH: 0293.35012
Digital Object Identifier: doi:10.1002/cpa.3160270403
[G] J. W. Gray, Some global properties of contact structures, Ann. of Math. (2) 69 (1959), 421–450.
Mathematical Reviews (MathSciNet): MR22:3016
Zentralblatt MATH: 0092.39301
Digital Object Identifier: doi:10.2307/1970192
JSTOR: links.jstor.org
[H] R. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), no. 2, 255–306.
Mathematical Reviews (MathSciNet): MR84a:53050
Zentralblatt MATH: 0504.53034
Project Euclid: euclid.jdg/1214436922
[JL] D. Jerison and J. M. Lee, The Yamabe problem on CR manifolds, J. Differential Geom. 25 (1987), no. 2, 167–197.
Mathematical Reviews (MathSciNet): MR88i:58162
Zentralblatt MATH: 0661.32026
Project Euclid: euclid.jdg/1214440849
[K] S. Kobayashi, Transformation Groups in Differential Geometry, Springer-Verlag, Berlin, 1972.
Mathematical Reviews (MathSciNet): MR50:8360
Zentralblatt MATH: 0246.53031
[L] J. M. Lee, Pseudo-Einstein structures on CR manifolds, Amer. J. Math. 110 (1988), no. 1, 157–178.
Mathematical Reviews (MathSciNet): MR89f:32034
Zentralblatt MATH: 0638.32019
Digital Object Identifier: doi:10.2307/2374543
JSTOR: links.jstor.org
[Li] J. L. Lions, Équations différentielles opérationnelles et problèmes aux limites, Die Grundlehren der mathematischen Wissenschaften, Bd. 111, Springer-Verlag, Berlin, 1961.
Mathematical Reviews (MathSciNet): MR27:3935
Zentralblatt MATH: 0098.31101
[Lu1] R. Lutz, Sur l'existence de certaines formes différentielles remarquables sur la sphère $S\sp{3}$, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1597–A1599.
Mathematical Reviews (MathSciNet): MR42:6741
Zentralblatt MATH: 0194.53201
[Lu2] R. Lutz, Structures de contact sur les fibrés principaux en cercles de dimension trois, Ann. Inst. Fourier (Grenoble) 27 (1977), no. 3, ix, 1–15.
Mathematical Reviews (MathSciNet): MR57:17668
Zentralblatt MATH: 0328.53024
[M] J. Martinet, Formes de contact sur les variétés de dimension $3$, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Springer, Berlin, 1971, 142–163. Lecture Notes in Math., Vol. 209.
Mathematical Reviews (MathSciNet): MR50:3263
Zentralblatt MATH: 0215.23003
[Ta] N. Tanaka, A Differential Geometric Study on Strongly Pseudo-Convex Manifolds, Kinokuniya Co. Ltd., Tokyo, 1975.
Mathematical Reviews (MathSciNet): MR53:3361
Zentralblatt MATH: 0331.53025
[T1] F. Treves, Basic Linear Partial Differential Equations, Academic Press, New York, 1975.
Mathematical Reviews (MathSciNet): MR56:6063
Zentralblatt MATH: 0305.35001
[T2] F. Treves, Introduction to Pseudodifferential and Fourier Integral Operators, Vol. 1: Pseudodifferential Operators, Plenum Press, New York, 1980.
Mathematical Reviews (MathSciNet): MR82i:35173
Zentralblatt MATH: 0453.47027
[W] S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geom. 13 (1978), no. 1, 25–41.
Mathematical Reviews (MathSciNet): MR80e:32015
Zentralblatt MATH: 0379.53016
Project Euclid: euclid.jdg/1214434345

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