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Einstein hypersurfaces of Kählerian C-spaces

Published online by Cambridge University Press:  22 January 2016

Yusuke Sakane  and
Masaru Takeuchi
Yusuke Sakane
Affiliation:
Osaka University
Masaru Takeuchi
Affiliation:
Osaka University
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A compact simply connected homogeneous complex manifold is called a C-space. A C-space is said to be kählerian if it carries a Kähler metric. It is known (Matsushima [7]) that a kählerian C-space has always an Einstein Kähler metric which is essentially unique.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 78 , May 1980 , pp. 153 - 175
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

[1] Borel, A. and Hirzebruch, F., Characteristic classes and homogeneous spaces I, Amer. J. Math. 80 (1958), 458–538.Google Scholar
[2] Bott, R., Homogeneous vector bundles, Ann. Math. 66 (1957), 203–248.Google Scholar
[3] Hano, J., Einstein complete intersections in complex projective space, Math. Ann. 216 (1975), 197–208.Google Scholar
[4] Hirzebruch, F., Topological Methods in Algebraic Geometry, Springer Verlag, New-York, 1966.Google Scholar
[5] Ise, M., Some properties of complex analytic vector bundles over compact complex homogeneous spaces, Osaka Math. J. 12 (1960), 217–252.Google Scholar
[6] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry II, Interscience, New York, 1969.Google Scholar
[7] Matsushima, Y., Remarks on Kähler-Einstein manifolds, Nagoya Math. J. 46 (1972), 161–173.Google Scholar
[8] Sakane, Y., On hypersurfaces of a complex Grassman manifold Gm+n, n(C), Osaka J. Math., 16 (1979), 71–95.Google Scholar
[9] Smyth, B., Differential geometry of complex hypersurfaces, Ann. Math. 85 (1967), 246–266.Google Scholar
[10] Takeuchi, M., Homogeneous Kähler submaniiolds in complex projective spaces, Japanese J. Math. New series, 4 (1978), 171–219.Google Scholar