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Some Involutive Structures in Analysis and Geometry

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Analysis and Geometry in Several Complex Variables

Part of the book series: Trends in Mathematics ((TM))

Abstract

An involutive structure on a smooth manifold is a complex subbundle T 0,1 of the complexified tangent bundle, closed under Lie bracket: [T 0,1,T 0,1] ⊆ T 0,1. For the general theory see [6, 16, 25]. Here are some examples.

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References

  1. T.N. Bailey and M.G. Eastwood, Zero-energy fields on real projective space, Geom. Dedicata, 67(1997), 245–258.

    Article  MathSciNet  MATH  Google Scholar 

  2. T.N. Bailey, M.G. Eastwood, A.R. Gover, and L.J. Mason, The Funk transform as a Penrose transform, Math. Proc. Camb. Phil. Soc., 125(1999), 67–81.

    Article  MathSciNet  MATH  Google Scholar 

  3. T.N. Bailey, M.G. Eastwood, and M.A. Singer, The Penrose Transform for Non-holomorphic Correspondences, in preparation.

    Google Scholar 

  4. M.S. Baouendi and F. Treves, A microlocal version of Bochner’s tube theorem, Indiana Math. Jour. 31 (1982), 885–895.

    Article  MathSciNet  MATH  Google Scholar 

  5. C.H. Chang, Hypoanalyticity with vanishing Levi form, Bull. Inst. Math. Acad. Sinica 13 (1985), 123–136.

    MathSciNet  MATH  Google Scholar 

  6. P.D. Cordaro and F. Treves, Hyperfunctions on Hypo-analytic Manifolds, Ann. Math. Stud. vol. 136, Princeton University Press, 1994.

    MATH  Google Scholar 

  7. M.G. Eastwood, The generalised Penrose-Ward transform, Math. Proc. Camb. Phil. Soc. 97 (1985), 165–187.

    Article  MathSciNet  MATH  Google Scholar 

  8. M.G. Eastwood, Introduction to Penrose transform, The Penrose Transform and Analytic Cohomology in Representation Theory, Cont. Math. vol. 154, Amer. Math. Soc. 1993, pp. 71–75.

    Google Scholar 

  9. M.G. Eastwood, Notes on conformai differential geometry, Suppl. Rendiconti Circolo Mat. Palermo 43 (1996), 57–76.

    MathSciNet  Google Scholar 

  10. M.G. Eastwood, Complex methods in real integral geometry, Suppl. Rendiconti Circolo Mat. Palermo 46 (1997), 55–71.

    Google Scholar 

  11. M.G. Eastwood, Some examples of the Penrose transform, R.I.M.S. Kokyuroku, Kyoto University, 1058 (1998), 22–28.

    MathSciNet  MATH  Google Scholar 

  12. M.G. Eastwood and C.R. Graham, The involutive structure on the blow-up onn inn, Comm. Anal. Geom., to appear.

    Google Scholar 

  13. M.G. Eastwood and C.R. Graham, An edge-of-the-wedge theorem for CR functions, in preparation.

    Google Scholar 

  14. RR. Garabedian, An unsolvable equation, Proc. A.M.S. 25 (1970), 207–208.

    MathSciNet  MATH  Google Scholar 

  15. C.R. Graham, private communication.

    Google Scholar 

  16. N. Hanges and H. Jacobowitz, Involutive structures on compact manifolds, Amer. Jour. Math. 177 (1995), 491–522.

    Article  MathSciNet  Google Scholar 

  17. L. Hörmander, An Introduction to Complex Analysis in Several Variables, Van Nostrand 1966, North-Holland 1973, 1990.

    MATH  Google Scholar 

  18. F. John, The ultrahyperbolic differential equation with four independent variables, Duke Math. Jour. 4 (1938), 300–322.

    Article  Google Scholar 

  19. H. Komatsu, A local version of Bochner’s tube theorem, Jour. Fac. Sci. Univ. Tokyo, Sect. 1A Math. 19 (1972), 201–214.

    MathSciNet  MATH  Google Scholar 

  20. H. Lewy, On the local character of the solution of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, Ann. Math. 64 (1956), 514–522.

    Article  MathSciNet  MATH  Google Scholar 

  21. H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. Math. 66 (1957), 155–158.

    Article  MathSciNet  Google Scholar 

  22. R. Michel, Problèmes d’analyse géométriques liés à la conjecture de Blaschke, Bull. Soc. Math. France 101 (1973), 17–69.

    MathSciNet  MATH  Google Scholar 

  23. R. Michel, Sur quelques problèmes de géométrie globale des géodésiques, Bol. Soc. Bras. Mat. 9 (1978), 19–38.

    Article  MATH  Google Scholar 

  24. J.-P. Rosay, A propos de “wedges”et d’“edges,” et de prolongements holomorphes, Trans. A.M.S. 297 (1986), 63–72.

    MathSciNet  MATH  Google Scholar 

  25. F. Treves, Hypo-analytic Structures, Princeton University Press, 1992.

    MATH  Google Scholar 

  26. C. Tsukamoto, Infinitesimal Blaschke conjectures on projective spaces, Ann. Scient. Éc. Norm. Sup. 14 (1981), 339–356.

    MathSciNet  MATH  Google Scholar 

  27. V.S. Vladimirov, V.V. Zharinov, and A.G. Sergeev, Bogolyubov’s “edge of the wedge” theorem, its development and applications, Russian Math. Surveys 49:5 (1994), 51–65.

    Article  MathSciNet  MATH  Google Scholar 

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© 1999 Birkhäuser Boston

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Eastwood, M. (1999). Some Involutive Structures in Analysis and Geometry. In: Komatsu, G., Kuranishi, M. (eds) Analysis and Geometry in Several Complex Variables. Trends in Mathematics. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2166-1_2

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  • DOI: https://doi.org/10.1007/978-1-4612-2166-1_2

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7441-4

  • Online ISBN: 978-1-4612-2166-1

  • eBook Packages: Springer Book Archive

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