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Riemann Space with Two-Parametric Homogeneous Holonomy Group

Published online by Cambridge University Press:  22 January 2016

Minoru Kurita
Minoru Kurita*
Affiliation:
Mathematical Institute, Nagoya University
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The rotational part of the holonomy group of a Riemann space is called its homogeneous holonomy group. A Riemann space, whose homogeneous holonomy group is one-parametric, was investigated by Liber and an alternative treatment of the same problem was given by S. Sasaki [1]. I will treat here a Riemann space with two-parametric homogeneous holonomy group and prove the following theorem by the method analogous to that of [1]. I thank Prof. T. Ootuki for his kind advice.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 4 , June 1952 , pp. 35 - 42
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1952

References

[1] Sasaki, S.: An alternative proof of Liber’s theorem, Proc. Japan Acad, Vol. 27 (1951).Google Scholar
[2] Cartan, E.: Leçon sur la géométrie des espaces de Riemann (Paris, Gathier-Villars. 1946).Google Scholar