Homogeneous hypersurfaces in Kähler C-spaces with b2=1

Kazuhiro KONNO

doi:10.2969/jmsj/04040687

Homogeneous hypersurfaces in Kähler C-spaces with b₂=1

Kazuhiro KONNO

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JOURNAL FREE ACCESS

1988 Volume 40 Issue 4 Pages 687-703

DOI https://doi.org/10.2969/jmsj/04040687

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Published: 1988 Received: May 28, 1987 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 : Homogeneous hypersurfaces in Kähler C-spaces with b₂=1
Right : Homogeneous hypersurfaces in Kähler C-spaces with b₂=1

Date of correction: October 20, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Mathematical Institute Tohoku Univeristy

Right :
1) Mathematical Institute Tôhoku University

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) C. Borcea, Smooth global complete intersections in certain homogeneous complex manifolds, J. Reine Angew. Math., 344 (1983), 65-70.
2) A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, Amer. J. Math., 80 (1958), 458-538.
3) A. Borel and R. Remmert, Über kompakte homogene Kählersche Mannigfaltigkeiten, Math. Ann., 145 (1962), 429-439.
4) A. Borel and A. Weil, Représentations linéaires et espaces homogènes kählériensdes groups de Lie compacts, Séminaire Bourbaki exp., 100 (1954).
5) R. Bott, Homogeneous vector bundles, Ann. of Math., 66 (1957), 203-248.
6) J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, 1972.
7) Y. Kimura, On the hypersurfaces of Hermitian symmetric spaces of compact type, Osaka J. Math., 16 (1979), 97-119, II, Osaka J. Math., 17 (1980), 455-469.
8) Y. Kimura, A hypersurface of the irreducible Hermitian symmetric space of type EIII, Osaka J. Math., 16 (1979), 431-438.
9) Y. Kimura, On the hypersurfaces of Kähler C-spaces, Kobe Shôka-daigaku Jinbunronshû, 16 (1980), 1-15, (in Japanese).
10) K. Konno, Infinitesimal Torelli theorem for complete intersections in certain homogeneous Kähler manifolds, Tohoku Math. J., 38 (1986), 609-624.
11) B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math., 74 (1961), 329-387.
12) S. Mori and H. Sumihiro, On Hartshorne's conjecture, J. Math. Kyoto Univ., 18 (1978), 523-533.
13) H. Nakagawa and R. Takagi, On locally symmetric Kaehler submanifolds in a complex projective space, J. Math. Soc. Japan, 28 (1976), 638-667.
14) Y. Sakane, On non-singular hyperplane sections of some Hermitian symmetric spaces, Osaka J. Math., 22 (1985), 107-121.
15) H. C. Wang, Closed manifolds with homogeneous complex structures, Amer. J. Math., 76 (1954), 1-32.

Right : [1] C. Borcea, Smooth global complete intersections in certain homogeneous complex manifolds, J. Reine Angew. Math., 344 (1983), 65-70.
[2] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, Amer. J. Math., 80 (1958), 458-538.
[3] A. Borel and R. Remmert, Über kompakte homogene Kählersche Mannigfaltigkeiten, Math. Ann., 145 (1962), 429-439.
[4] A. Borel and A. Weil, Représentations linéaires et espaces homogènes kählériens des groups de Lie compacts, Séminaire Bourbaki exp., 100 (1954).
[5] R. Bott, Homogeneous vector bundles, Ann. of Math., 66 (1957), 203-248.
[6] J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, 1972.
[7] Y. Kimura, On the hypersurfaces of Hermitian symmetric spaces of compact type, Osaka J. Math., 16 (1979), 97-119, II, Y. Kimura, On the hypersurfaces of Hermitian symmetric spaces of compact type, Osaka J. Math., 17 (1980), 455-469.
[8] Y. Kimura, A hypersurface of the irreducible Hermitian symmetric space of type EIII, Osaka J. Math., 16 (1979), 431-438.
[9] Y. Kimura, On the hypersurfaces of Kähler C-spaces, Kobe Shôka-daigaku Jinbunronshû, 16 (1980), 1-15, (in Japanese).
[10] K. Konno, Infinitesimal Torelli theorem for complete intersections in certain homogeneous Kähler manifolds, Tôhoku Math. J., 38 (1986), 609-624.
[11] B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math., 74 (1961), 329-387.
[12] S. Mori and H. Sumihiro, On Hartshorne's conjecture, J. Math. Kyoto Univ., 18 (1978), 523-533.
[13] H. Nakagawa and R. Takagi, On locally symmetric Kaehler submanifolds in a complex projective space, J. Math. Soc. Japan, 28 (1976), 638-667.
[14] Y. Sakane, On non-singular hyperplane sections of some Hermitian symmetric spaces, Osaka J. Math., 22 (1985), 107-121.
[15] H. C. Wang, Closed manifolds with homogeneous complex structures, Amer. J. Math., 76 (1954), 1-32.

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