Complex Laplacians on compact complex homogeneous spaces

Hajime URAKAWA

doi:10.2969/jmsj/03340619

Hajime URAKAWA

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JOURNAL FREE ACCESS

1981 Volume 33 Issue 4 Pages 619-638

DOI https://doi.org/10.2969/jmsj/03340619

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Published: 1981 Received: February 01, 1980 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) M. Berger, Eigenvalues of the Laplacian, Amer. Math. Soc. Proc. Pure Math., 16 (1970), 121-125.
2) M, Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, Springer, Berlin, 1971.
3) A. Borel, Kaehlerian coset spaces of semi-simple Lie groups, Proc. Nat. Acad. Sci. U.S.A., 40 (1954), 1147-1151.
4) A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, Amer. J. Math., 80 (1958), 458-538.
5) A. Froelicher, Zur Differentialgeometrie der komplexen Structuren, Math. Ann., 129 (1955), 50-95.
6) P. B. Gilkey, Spectral geometry and the Kaehler condition for complex manifolds, Invent. Math., 26 (1974), 231-258.
7) P. B. Gilkey, Correction to spectral geometry and the Kaehler condition for complex manifolds, Invent. Math., 29 (1975), 81-82.
8) J. Hano and S. Kobayashi, A fibering of a class of homogeneous complex manifolds, Trans. Amer. Math. Soc., 94 (1960), 233-243.
9) Harish-Chandra, Representations of semi-simple Lie groups IV, Amer. J. Math., 77 (1955), 743-777.
10) S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962.
11) S. Kobayashi and K. Nomizu, Foundations of differential geometry II, Interscience Publishers, New York, 1969.
12) K. Kodaira and J. Morrow, Complex manifolds, Holt, Rinehart & Winston, Inc., 1971.
13) Y. Matsushima and S. Murakami, On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds, Ann, of Math., 78(2), (1963), 365-416.
14) M. Takeuchi, Modern theory of spherical functions (in Japanese), Iwanami, Tokyo, 1975.
15) H. C. Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math., 76 (1954), 1-32.
16) H. C. Wang, Complex parallelisable manifold, Proc. Amer. Math. Soc., 51 (1954), 771-776.
17) K. Tsukada, Eigenvalues of the Laplacian on Calabi-Eckmann manifolds (a preprint).
18) J. A. Wolf and A. Gray, Homogeneous spaces defined by Lie group automorphisms I, II, J. Differential Geometry, 2 (1968), 77-114, 115-159.

Right : [1] M. Berger, Eigenvalues of the Laplacian, Amer. Math. Soc. Proc. Pure Math., 16 (1970), 121-125.
[2] M, Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, Springer, Berlin, 1971.
[3] A. Borel, Kaehlerian coset spaces of semi-simple Lie groups, Proc. Nat. Acad. Sci. U. S. A., 40 (1954), 1147-1151.
[4] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, Amer. J. Math., 80 (1958), 458-538.
[5] A. Froelicher, Zur Differentialgeometrie der komplexen Structuren, Math. Ann., 129 (1955), 50-95.
[6] P. B. Gilkey, Spectral geometry and the Kaehler condition for complex manifolds, Invent. Math., 26 (1974), 231-258.
[7] P. B. Gilkey, Correction to spectral geometry and the Kaehler condition for complex manifolds, Invent. Math., 29 (1975), 81-82.
[8] J. Hano and S. Kobayashi, A fibering of a class of homogeneous complex manifolds, Trans. Amer. Math. Soc., 94 (1960), 233-243.
[9] Harish-Chandra, Representations of semi-simple Lie groups IV, Amer. J. Math., 77 (1955), 743-777.
[10] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962.
[11] S. Kobayashi and K. Nomizu, Foundations of differential geometry II, Interscience Publishers, New York, 1969.
[12] K. Kodaira and J. Morrow, Complex manifolds, Holt, Rinehart & Winston, Inc., 1971.
[13] Y. Matsushima and S. Murakami, On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds, Ann, of Math., 78 (2), (1963), 365-416.
[14] M. Takeuchi, Modern theory of spherical functions (in Japanese), Iwanami, Tokyo, 1975.
[15] H. C. Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math., 76 (1954), 1-32.
[16] H. C. Wang, Complex parallelisable manifold, Proc. Amer. Math. Soc., 51 (1954), 771-776.
[17] K. Tsukada, Eigenvalues of the Laplacian on Calabi-Eckmann manifolds (a preprint).
[18] J. A. Wolf and A. Gray, Homogeneous spaces defined by Lie group automorphisms I, II, J. Differential Geometry, 2 (1968), 77-114, 115-159.

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