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On the Holonomy Group of the Conformally Flat Riemannian Manifold

Published online by Cambridge University Press:  22 January 2016

Minoru Kurita
Minoru Kurita*
Affiliation:
Mathematical Institute, Nagoya University
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The main purpose of the present paper is to show that the local homogeneous holonomy group of the conformally flat Riemannian manifold is the full rotation group with some exceptions.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 9 , October 1955 , pp. 161 - 171
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1955

References

[1] Nijenhuis, A., On the holonomy groups of linear connections I a. General properties of affine connections, Indag. Math., 15, pp. 233–240 (1953).Google Scholar
[2] Yano, K. and Mogi, I., On the real representation of Kaehlerian manifolds, Ann. of Math., 61, pp. 170–189 (1955).Google Scholar
[3] Chern, S. S., Topics in differential geometry, Princeton (1951).Google Scholar
[4] Kurita, M., On conformal Riemann spaces, Jour. Math. Soc. Japan, 7, pp. 13–31 (1955).Google Scholar
[5] Kobayasi, S., Holonomy groups of hypersurfaces, to appear in the next issue of Nagoya Math. Journ.Google Scholar