Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SOLVABILITY OF OVERDETERMINED PDE SYSTEMS THAT ADMIT A COMPLETE PROLONGATION AND SOME LOCAL PROBLEMS IN CR GEOMETRY

  • Han, Chong-Kyu (Department of Mathematics Seoul National University)
  • Published : 2003.07.01
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Abstract

We study the existence of solutions for overdetermined PDE systems that admit prolongation to a complete system. We reduce the problem to a Pfaffian system on a submanifold of the jet space of unknown functions and then express the integrability conditions in terms of the coefficients of the original system. As possible applications we present some local problems in CR geometry: determining the CR embeddibility into spheres and the existence of infinitesimal CR automorphisms.

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References

  1. Exterior differential systems R.Bryant;S.S.Chern;R.Gardner;H.Goldschmidt;P.Griffiths
  2. Proc. Symp. Pure Math. v.30 Real hypersurfaces in complex manifolds D.Burns;S.Schnider
  3. Rocky Mt. J. Math. v.23 Compatibility equations for isometric embeddings of Riemannian manifolds C.K.Cho;C.K.Han https://doi.org/10.1216/rmjm/1181072490
  4. J. Korean Math. Soc. v.39 no.1 Finiteness of infinitesimal deformations of CR mappings of CR manifolds of nondegenerate Levi form C.K.Cho;C.K.Han https://doi.org/10.4134/JKMS.2002.39.1.091
  5. Acta Math. v.133 Real hypersurfaces in complex manifolds S.S.Chern;J.K.Moser https://doi.org/10.1007/BF02392146
  6. Ann. of Math. Stud. no.114 Differential systems and isometric embeddings P.Griffiths;G.Jensen
  7. Math. Ann. v.309 Complete differential system for the mappings of CR manifolds of nondegenerate Levi forms C.K.Han
  8. J. Koeran Math. Soc. v.37 no.2 Equivalence problem and complete system of finite order C.K.Han
  9. An introduction to CR structures H.Jacobowitz
  10. J. Korean Math. Soc. v.39 no.2 Complete prolongation and the Frobenius integrability for overdetermined systems of partial differential equations J.S.Cho;C.K.Han https://doi.org/10.4134/JKMS.2002.39.2.237
  11. Local embeddibility of pseudo-hermitian manifolds into spheres S.Y.Kim
  12. Amer. J. Math. v.79 On E. Cartan's prolongation theorem of exterior differential systems M.Kuranishi https://doi.org/10.2307/2372381
  13. Existence of infinitesimal automorphisms in the three dimensional CR manifolds of nondegenerate Leve form H.D.Lee
  14. CR embeddibility of ellipsoids into spheres J.W.Oh
  15. Applications of Lie groups to differential equations P.J.Olver
  16. Publish or Perish v.2 A comprehensive introduction to differential geometry M.Spivak
  17. J. Math. Soc. Japan v.14 On the pseudo-conformal geometry of hypersurfaces of the space of n complex variables N.Tanaka https://doi.org/10.2969/jmsj/01440397
  18. Japan. J. Math. v.2 On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections N.Tanaka https://doi.org/10.4099/math1924.2.131
  19. Indiana Univ. Math. J. v.28 The rigidity of CR hypersurfaces in a sphere S.webster https://doi.org/10.1512/iumj.1979.28.28027
  20. Hokkaido univ. Preprint Series in Math. v.524 Geometry of higher order differential equations of finite type associated with symmetric spaces K.Yamaguchi;T.Yatsui

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  1. COMPLEX SUBMANIFOLDS IN REAL HYPERSURFACES vol.47, pp.5, 2010, https://doi.org/10.4134/JKMS.2010.47.5.1001
  2. Local embeddability of CR manifolds into spheres vol.344, pp.1, 2009, https://doi.org/10.1007/s00208-008-0302-8
  3. Infinitesimal Isometries Along Curves and Generalized Jacobi Equations vol.23, pp.1, 2013, https://doi.org/10.1007/s12220-011-9250-8