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Studies on Riemannian Homogeneous Spaces

Published online by Cambridge University Press:  22 January 2016

Katsumi Nomizu
Katsumi Nomizu*
Affiliation:
Mathematical Institute, Nagoya University
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The purpose of the present paper is to give the details of the results announced in the C. R. notes [7], [8] and [9].

In I which corresponds to [7], we shall develop a method for the study of affine transformations of a Riemannian manifold and prove Lemma 5 which is fundamental for the results in I and II. This part of our work has been motivated by a result of K. Yano [12] stating that the largest connected group of affine transformations of a compact orientable Riemannian manifold consists of isometries. Our method will have further applications to some other problems concerning or involving the connected group of isometries of a Riemannian manifold (for example, [10]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 9 , October 1955 , pp. 43 - 56
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1955

References

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