On curvature properties of Kähler C-spaces

Mitsuhiro ITOH

doi:10.2969/jmsj/03010039

Mitsuhiro ITOH

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JOURNAL FREE ACCESS

1978 Volume 30 Issue 1 Pages 39-71

DOI https://doi.org/10.2969/jmsj/03010039

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Published: 1978 Received: May 17, 1976 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: CITATION Details: Wrong : 1) A. Borel, Kählerian coset spaces of semi-simple Lie groups, Proc. Nat. Acad. Sci. U.S.A., 40 (1954), 1147-1151.
2) A. Borel, On the curvature tensor of the Hermitian symmetric manifolds, Ann. of Math., 71 (1960), 508-521.
3) A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, Amer. J. Math., 80 (1958), 458-538.
4) N. Bourbaki, Groupes et algèbres de Lie, IV, V et VI, Eléments de Mathématique, Hermann, Paris, 1968.
5) E. Calabi and E. Vesentini, On compact locally symmetric Kaehler manifolds, Ann. of Math., 71 (1960), 472-507.
6) S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962.
7) M. Ise, The theory of symmetric spaces II, Sugaku, 13 (1961), 88-107 (in Japanese).
8) S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, II, Interscience publishers, 1969.
9) Y. Matsushima, Sur les espaces homogènes kähleriens d'un groupe de Lie réductif, Nagoya Math. J., 11 (1957), 53-60.
10) H. Nakagawa and R. Takagi, On locally symmetric Kaehler submanifolds in a complex projective space, J. Math. Soc. Japan, 28 (1976), 638-667.
11) K. Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math., 76 (1954), 33-65.
12) B. Smyth, Differential geometry of complex hypersurfaces, Ann. of Math., 85 (1967), 246-266.
13) H. C. Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math., 76 (1954), 1-32.

Right : [1] A. Borel, Kählerian coset spaces of semi-simple Lie groups, Proc. Nat. Acad. Sci. U. S. A., 40 (1954), 1147-1151.
[2] A. Borel, On the curvature tensor of the Hermitian symmetric manifolds, Ann. of Math., 71 (1960), 508-521.
[3] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, Amer. J. Math., 80 (1958), 458-538.
[4] N. Bourbaki, Groupes et algèbres de Lie, IV, V et VI, Eléments de Mathématique, Hermann, Paris, 1968.
[5] E. Calabi and E. Vesentini, On compact locally symmetric Kaehler manifolds, Ann. of Math., 71 (1960), 472-507.
[6] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962.
[7] M. Ise, The theory of symmetric spaces II, Sugaku, 13 (1961), 88-107 (in Japanese).
[8] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, II, Interscience publishers, 1969.
[9] Y. Matsushima, Sur les espaces homogènes kähleriens d'un groupe de Lie réductif, Nagoya Math. J., 11 (1957), 53-60.
[10] H. Nakagawa and R. Takagi, On locally symmetric Kaehler submanifolds in a complex projective space, J. Math. Soc. Japan, 28 (1976), 638-667.
[11] K. Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math., 76 (1954), 33-65.
[12] B. Smyth, Differential geometry of complex hypersurfaces, Ann. of Math., 85 (1967), 246-266.
[13] H. C. Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math., 76 (1954), 1-32.

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