On homogeneous Kähler manifolds of solvable Lie groups

Hirohiko SHIMA

doi:10.2969/jmsj/02530422

Hirohiko SHIMA

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JOURNAL FREE ACCESS

1973 Volume 25 Issue 3 Pages 422-445

DOI https://doi.org/10.2969/jmsj/02530422

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Published: 1973 Received: April 24, 1972 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S.G. Gindikin, I.I. Pjateckii-Šapiro and E.B. Vinberg, Homogeneous Kähler manifolds, in “Geometry of Homogeneous Bounded Domains”, Centro Int. Math. Estivo, 3 Ciclo, Urbino, Italy, 1967, 3-87.
2) J. Hano, On kaehlerian homogeneous spaces of unimodular Lie groups, Amer. 3. Math., 79 (1957), 885-900.
3) J. Hano, Equivariant projective immersion of a complex coset space with non-degenerate canonical hermitian form, Scripta Math., 29 (1971).
4) S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962.
5) S. Kaneyuki, On the automorphism groups of homogeneous bounded domains, J. Fac. Sci. Univ. Tokyo, 14 (1967), 89-130.
6) S. Kobayashi and K. Nomizu, On automorphisms of a Kählerian structure, Nagoya Math. J., 11 (1957), 115-124.
7) S. Kobayashi and K. Nomizu, Foundations of differential geometry, II, Interscience Publishers, New York, 1969.
8) J.L. Koszul, Sur la forme hermitienne canonique des espaces homogènes complexes, Canad. J. Math., 7 (1955), 562-576.
9) I.I. Pjateckii-Šapiro, Bounded homogeneous domains in n-dimensional complex space, Izv. Akad. Nauk SSSR Ser. Math., 26 (1962), 107-124; English transl., Amer. Math. Soc. Transl., (2) 43 (1964), 299-320.
10) I.I. Pjateckii-Šapiro, The structure of j-algebras, Izv. Akad. Nauk SSSR Ser. Math., 26 (1962), 453-484; English transl., Amer. Math. Soc. Transl., (2) 55 (1966), 207-241.
11) H. Shima, On homogeneous complex manifolds with negative definite canonical hermitian form, Proc. Japan Acad., (3) 46 (1970), 209-211.
12) E.B. Vinberg, The Morozov-Borel theorem for real Lie groups, Dokl. Acad. Nauk SSSR, 141 (1961), 270-273; English transl., Soviet Math. Dokl., 2 (1961), 1416-1419.
13) E.B. Vinberg, S.G. Gindikin and I.I. Pjateckii-Šapiro, Classification and canonical realization of complex bounded homogeneous domains, Trudy Moscow Math. Obshch., 12 (1963), 359-388; English transl., Trans. Moscow Math. Soc., 12 (1963), 404-437.
14) E.B. Vinberg and S. G. Gindikin, Kaehlerian manifolds admitting a transitive solvable automorphism group, English transl., Math. Sb., 74 (116) (1967), 333-351.

Right : [1] S. G. Gindikin, I. I. Pjateckii-Šapiro and E. B. Vinberg, Homogeneous Kähler manifolds, in “Geometry of Homogeneous Bounded Domains”, Centro Int. Math. Estivo, 3 Ciclo, Urbino, Italy, 1967, 3-87.
[2] J. Hano, On kaehlerian homogeneous spaces of unimodular Lie groups, Amer. J. Math., 79 (1957), 885-900.
[3] J. Hano, Equivariant projective immersion of a complex coset space with non-degenerate canonical hermitian form, Scripta Math., 29 (1971).
[4] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962.
[5] S. Kaneyuki, On the automorphism groups of homogeneous bounded domains, J. Fac. Sci. Univ. Tokyo, 14 (1967), 89-130.
[6] S. Kobayashi and K. Nomizu, On automorphisms of a Kählerian structure, Nagoya Math. J., 11 (1957), 115-124.
[7] S. Kobayashi and K. Nomizu, Foundations of differential geometry, II, Interscience Publishers, New York, 1969.
[8] J. L. Koszul, Sur la forme hermitienne canonique des espaces homogènes complexes, Canad. J. Math., 7 (1955), 562-576.
[9] I. I. Pjateckii-Šapiro, Bounded homogeneous domains in n-dimensional complex space, Izv. Akad. Nauk SSSR Ser. Math., 26 (1962), 107-124; English transl., Amer. Math. Soc. Transl., (2) 43 (1964), 299-320.
[10] I. I. Pjateckii-Šapiro, The structure of j-algebras, Izv. Akad. Nauk SSSR Ser. Math., 26 (1962), 453-484; English transl., Amer. Math. Soc. Transl., (2) 55 (1966), 207-241.
[11] H. Shima, On homogeneous complex manifolds with negative definite canonical hermitian form, Proc. Japan Acad., (3) 46 (1970), 209-211.
[12] E. B. Vinberg, The Morozov-Borel theorem for real Lie groups, Dokl. Acad. Nauk SSSR, 141 (1961), 270-273; English transl., Soviet Math. Dokl., 2 (1961), 1416-1419.
[13] E. B. Vinberg, S. G. Gindikin and I. I. Pjateckii-Šapiro, Classification and canonical realization of complex bounded homogeneous domains, Trudy Moscow Math. Obshch., 12 (1963), 359-388; English transl., Trans. Moscow Math. Soc., 12 (1963), 404-437.
[14] E. B. Vinberg and S. G. Gindikin, Kaehlerian manifolds admitting a transitive solvable automorphism group, English transl., Math. Sb., 74 (116) (1967), 333-351.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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