Isotropy representations of semisimple symmetric spaces and homogeneous hypersurfaces

Jörg HAHN

doi:10.2969/jmsj/04020271

Jörg HAHN

著者情報

ジャーナルフリー

1988 年 40 巻 2 号 p. 271-288

DOI https://doi.org/10.2969/jmsj/04020271

詳細

Published: 1988 Received: 1986/11/17 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M. Berger, Les espaces symétriques non compacts, Ann. Sci. École Norm. Sup., 74 (1957), 85-177.
2) M. Cahen and N. Wallach, Lorentzian symmetric spaces, Bull. Amer. Math. Soc., 76 (1970), 585-591.
3) D. Ferus, H. Karcher and H.F. Münzner, Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z., 177 (1981), 479-502.
4) M. Goto and F.D. Grosshans, Semisimple Lie algebras, Dekker, New York, 1978.
5) J. Hahn, Homogene Hyperflächen in der pseudoriemannschen Geometrie, Bonn. Math. Schr., 172 (1986).
6) J. Hahn, Pseudo-riemannian isoparametric hypersurfaces and homogeneity, (in preparation).
7) S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978.
8) O. Loos, Symmetric spaces II, Benjamin, New York, 1969.
9) T. Matsuki, The orbits of affine symmetric spaces under the action of minimal parabolic subgroups, J. Math. Soc. Japan, 31 (1979), 331-356.
10) T. Matsuki and T. Oshima, Orbits on affine symmetric spaces under the action of the isotropy subgroups, J. Math. Soc. Japan, 32 (1980), 399-414.
11) W. Rossmann, The structure of semisimple symmetric spaces, Canad. J. Math., 31(1979), 157-180.
12) L.P. Rothschild, Orbits in a real reductive Lie algebra, Trans. Amer. Math. Soc., 168 (1972), 403-421.
13) R. Takagi and T. Takahashi, On the principal curvatures of homogeneous hypersurfaces in a sphere, Differential Geometry in honor of K. Yano, Kinokuniya, Tokyo, 1972, pp. 469-481.

Right : [1] M. Berger, Les espaces symétriques non compacts, Ann. Sci. École Norm. Sup., 74 (1957), 85-177.
[2] M. Cahen and N. Wallach, Lorentzian symmetric spaces, Bull. Amer. Math. Soc., 76 (1970), 585-591.
[3] D. Ferus, H. Karcher and H. F. Münzner, Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z., 177 (1981), 479-502.
[4] M. Goto and F. D. Grosshans, Semisimple Lie algebras, Dekker, New York, 1978.
[5] J. Hahn, Homogene Hyperflächen in der pseudoriemannschen Geometrie, Bonn. Math. Schr., 172 (1986).
[6] J. Hahn, Pseudo-riemannian isoparametric hypersurfaces and homogeneity, (in preparation).
[7] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978.
[8] O. Loos, Symmetric spaces II, Benjamin, New York, 1969.
[9] T. Matsuki, The orbits of affine symmetric spaces under the action of minimal parabolic subgroups, J. Math. Soc. Japan, 31 (1979), 331-356.
[10] T. Matsuki and T. Oshima, Orbits on affine symmetric spaces under the action of the isotropy subgroups, J. Math. Soc. Japan, 32 (1980), 399-414.
[11] W. Rossmann, The structure of semisimple symmetric spaces, Canad. J. Math., 31 (1979), 157-180.
[12] L. P. Rothschild, Orbits in a real reductive Lie algebra, Trans. Amer. Math. Soc., 168 (1972), 403-421.
[13] R. Takagi and T. Takahashi, On the principal curvatures of homogeneous hypersurfaces in a sphere, Differential Geometry in honor of K. Yano, Kinokuniya, Tokyo, 1972, pp. 469-481.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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