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Covariant derivatives on Kähler C-spaces

Published online by Cambridge University Press:  22 January 2016

Koji Tojo
Koji Tojo*
Affiliation:
Graduate School of Science and Technology, Chiba University, Chiba-shi, 263, Japan
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Let (M, g) be a Kähler C-space. R and ∇ denote the curvature tensor and the Levi-Civita connection of (M, g), respectively.

In [6], Takagi have proved that there exists an integer n such that

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 143 , September 1996 , pp. 31 - 57
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

[ 1 ] Freudenthal, Hans and de Vries, H., Linear Lie Groups, Academic Press, 1969.Google Scholar
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[ 3 ] Itoh, M., On curvature properties of Kähler C-spaces, J. Math. Soc. Japan, 30 (1976), 39–71.Google Scholar
[ 4 ] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry II, Interscience Publishers, 1969.Google Scholar
[ 5 ] Nomizu, K., Invariant affine connections on homogeneous spaces, Amer. J. Math., 76 (1954), 33–65.Google Scholar
[ 6 ] Takagi, R., On higher covariant derivatives of the curvature tensors of Kählerian C-spaces, Nagoya Math. J., 91 (1983), 1–18.Google Scholar
[ 7 ] Wolf, J. A., On the classification of hermitian symmetric spaces, J. Math. Mech., 13 (1964), 489–495.Google Scholar