Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Almost complex manifolds and Cartan's uniqueness theorem


Author: Kang-Hyurk Lee
Journal: Trans. Amer. Math. Soc. 358 (2006), 2057-2069
MSC (2000): Primary 32H02, 32Q60
DOI: https://doi.org/10.1090/S0002-9947-05-03973-5
Published electronically: December 20, 2005
MathSciNet review: 2197447
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We present a generalization of Cartan's uniqueness theorem to the almost complex manifolds.


References [Enhancements On Off] (What's this?)

  • 1. R.A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press, 1975. MR 0450957 (56:9247)
  • 2. M. Audin, J. Lafontaine, editors, Holomorphic curves in symplectic geometry, Progress in Mathematics, 117, Birkhäuser Verlag, Basel, 1994. MR 1274923 (95i:58005)
  • 3. A. Floer, H. Hofer, D. Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke. Math. J., 80 (1995), 251-292. MR 1360618 (96h:58024)
  • 4. P. Gauduchon, The canonical almost complex structure on the manifold of 1-jets of pseudo-holomorphic mappings between two almost complex manifolds, appendix to Chap. II in [2]. MR 1274923 (95i:58005)
  • 5. D. Gilbarg, N.S. Trudinger, Elliptic partial differential equations of second order, Second edition. Grundlehren der Mathematischen Wissenschaften, 224, Springer-Verlag, Berlin, 1983. MR 0737190 (86c:35035)
  • 6. J. Globevnik, Perturbing analytic discs attached to maximal real submanifold of $ \mathbb{C}^N$, Indag. Math., 7 (1996), 37-46. MR 1621348 (99b:32023)
  • 7. M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347.
  • 8. S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, 2 Marcel Dekker, Inc., New York, 1970. MR 0277770 (43:3503)
  • 9. S. Kobayashi, Hyperbolic complex spaces, Grundlehren der Mathematischen Wissenschaften, 318, Springer-Verlag, Berlin, 1998. MR 1635983 (99m:32026)
  • 10. B.S. Kruglikov, Existence of close pseudoholomorphic disks for almost complex manifolds and their application to the Kobayashi-Royden pseudonorm (Russian) Funktsional. Anal. i Prilozhen., 33 (1999), no. 1, 46-58, 96; translation in Funct. Anal. Appl., 33 (1999), no. 1, 38-48. MR 1711878 (2000i:32044)
  • 11. B.S. Kruglikov, M. Overholt, Pseudoholomorphic mappings and Kobayashi hyperbolicity, Differential Geom. Appl. 11 (1999), no. 3, 265-277. MR 1726542 (2000j:32042)
  • 12. D. McDuff, D. Salamon, $ J$-holomorphic curves and quantum cohomology, University Lecture Series, 6, American Mathematical Society, Providence, RI, 1994. MR 1286255 (95g:58026)
  • 13. R. Narasimhan, Several complex variables, Chicago Lectures in Mathematics, The University of Chicago Press, Chicago, 1971. MR 0342725 (49:7470)
  • 14. A. Newlander, L. Nirenberg, Complex analytic coordinates in almost complex manifolds, Ann. of Math., 65 (1957), 391-404. MR 0088770 (19:577a)
  • 15. A. Nijenhuis, W. Woolf, Some integration problems in almost-complex and complex manifolds, Ann. Math., 77 (1963), 424-489. MR 0149505 (26:6992)
  • 16. H.L. Royden, Remarks on the Kobayashi metric, Several complex variables, II (Proc. Internat. Conf., Univ. Maryland, College Park, Md., 1970), pp. 125-137. Lecture Notes in Math., Vol. 185, Springer, Berlin, 1971. MR 0304694 (46:3826)
  • 17. J.C. Sikorav, Some properties of holomorphic curves in almost complex manifolds, 165-189, in [2]. MR 1274929

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 32H02, 32Q60

Retrieve articles in all journals with MSC (2000): 32H02, 32Q60


Additional Information

Kang-Hyurk Lee
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Republic of Korea
Address at time of publication: Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, Republic of Korea
Email: nyawoo@postech.ac.kr

DOI: https://doi.org/10.1090/S0002-9947-05-03973-5
Received by editor(s): March 12, 2004
Published electronically: December 20, 2005
Additional Notes: This research was upported in part by Grant KRF-2002-070-C00005 (PI: K.T. Kim) from the Korea Research Foundation.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society