Complex structures on S1×S5

Masahide KATO

doi:10.2969/jmsj/02830550

Complex structures on S¹×S⁵

Masahide KATO

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JOURNAL FREE ACCESS

1976 Volume 28 Issue 3 Pages 550-576

DOI https://doi.org/10.2969/jmsj/02830550

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Published: 1976 Received: July 16, 1975 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Complex structures on S¹×S²
Right : Complex structures on S¹×S⁵

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) E. Brieskorn and A. Van de Ven, Some complex structures on products of homotopy spheres, Topology, 7 (1967), 389-393.
2) H. Grauert and R. Remmert, Komplexe Räume, Math. Ann., 136 (1958), 245-318.
3) Ma. Kato, Complex structures on S¹×S⁵, Proc. Japan Acad., 49 (1973), 575-577.
4) Ma. Kato, A generalization of Bieberbach's example, Proc. Japan Acad., 50 (1974), 329-333.
5) K. Kodaira, On compact analytic surfaces II, Ann. of Math., 77 (1963), 563-626.
6) K. Kodaira, On the structure of compact complex analytic surfaces I, Amer. J. Math., 86 (1964), 751-798.
7) K. Kodaira, On the structure of compact complex analytic surfaces IV, Amer. J. Math., 90 (1968), 1048-1066.
8) H.-S. Ling, Extending families of pseudoconcave complex spaces, Math. Ann., 204 (1973), 13-48.
9) P. Orlik and P. Wagreich, Isolated singularities of algebraic surfaces with C*-action, Ann. of Math., 93 (1971), 205-228.
10) M. Raynaud, Géométrie Algébrique et Géométrie Analytique, Séminaire de Géométrie Algébrique 1, Exposé XII, (1960-61), IHES, Lecture Notes in Math., 224, Springer, 1971.
11) L. Reich, Das Typenproblem bei formal-biholomorphen Abbildungen mit anziehendem Fixpunkt, Math. Ann., 179 (1969), 227-250.
12) L. Reich, Normalformen biholomorpher Abbildungen mit anziehendem Fixpunkt, Math. Ann., 180 (1969), 233-255.
13) W. Rudin, A geometric criterion for algebraic varieties, J. Math. Mech., 17(7) (1968), 671-683.
14) Y.-T. Siu, Extending coherent analytic sheaves, Ann. of Math., 90 (1969), 108-143.
15) Y.-T. Siu, The 1-convex generalization of Grauert's direct image theorem, Math. Ann., 190 (1971), 203-214.
16) K. Yosida, Functional Analysis, Springer, 1964.

Right : [1] E. Brieskorn and A. Van de Ven, Some complex structures on products of homotopy spheres, Topology, 7 (1967), 389-393.
[2] H. Grauert and R. Remmert, Komplexe Räume, Math. Ann., 136 (1958), 245-318.
[3] Ma. Kato, Complex structures on S¹×S⁵, Proc. Japan Acad., 49 (1973), 575-577.
[4] Ma. Kato, A generalization of Bieberbach's example, Proc. Japan Acad., 50 (1974), 329-333.
[5] K. Kodaira, On compact analytic surfaces II, Ann. of Math., 77 (1963), 563-626.
[6] K. Kodaira, On the structure of compact complex analytic surfaces I, Amer. J. Math., 86 (1964), 751-798.
[7] K. Kodaira, On the structure of compact complex analytic surfaces IV, Amer. J. Math., 90 (1968), 1048-1066.
[8] H. -S. Ling, Extending families of pseudoconcave complex spaces, Math. Ann., 204 (1973), 13-48.
[9] P. Orlik and P. Wagreich, Isolated singularities of algebraic surfaces with C-action, Ann. of Math., 93 (1971), 205-228.
[10] M. Raynaud, Géométrie Algébrique et Géométrie Analytique, Séminaire de Géométrie Algébrique 1, Exposé XII, (1960-61), IHES, Lecture Notes in Math., 224, Springer, 1971.
[11] L. Reich, Das Typenproblem bei formal-biholomorphen Abbildungen mit anziehendem Fixpunkt, Math. Ann., 179 (1969), 227-250.
[12] L. Reich, Normalformen biholomorpher Abbildungen mit anziehendem Fixpunkt, Math. Ann., 180 (1969), 233-255.
[13] W. Rudin, A geometric criterion for algebraic varieties, J. Math. Mech., 17 (7) (1968), 671-683.
[14] Y. -T. Siu, Extending coherent analytic sheaves, Ann. of Math., 90 (1969), 108-143.
[15] Y. -T. Siu, The 1-convex generalization of Grauert's direct image theorem, Math. Ann., 190 (1971), 203-214.
[16] K. Yosida, Functional Analysis, Springer, 1964.

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