Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-03T08:55:12.562Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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