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Holomorphic functions on almost complex manifolds

김혜선|한종규
대한수학회 (The Korean Mathematical Society)|2012.03|대한수학회지 (Journal of the KMS)|제49권 제2호|pp. 379-394

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키워드

Nijenhuis tensoralmost complex manifoldsJ-holomorphic functionsNewlander-Nirenberg theorem.
주제분류수학

초록

Given an almost complex structure (Cm, J), m  2, that is de ned by setting  = dz + a dz , = 1,...,m, to be (1; 0)-forms,we nd conditions on (a ) for the existence of holomorphic functions and classify the almost complex structures by type (; q). Then we determine types for several examples in C2 and C3 including the natural almost complex structure on S6.

Abstract

Given an almost complex structure (Cm, J), m  2, that is de ned by setting  = dz + a dz , = 1,...,m, to be (1; 0)-forms,we nd conditions on (a ) for the existence of holomorphic functions and classify the almost complex structures by type (; q). Then we determine types for several examples in C2 and C3 including the natural almost complex structure on S6.

참고문헌 (15)

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  10. "Complete prolongation for infinitesimal automorphisms on almost complex manifolds", MATHEMATISCHE ZEITSCHRIFT, 264, pp.913~925 (2010), SPRINGER
  11. B. S. Krugilov, "Nijenhuis tensors and obstructions to constructing pseudoholomorphic mappings", Mathematical Notes, 63, pp.476~493 (1998)
  12. O. Muskarov, "Almost complex manifolds without almost holomorphic functions", C. R. Acad. Bulgare Sci, 34(9), pp.1225~1228 (1981)
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