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Canonical Connections and Pontrjagin Classes

Published online by Cambridge University Press:  22 January 2016

Shoshichi Kobayashi
Shoshichi Kobayashi*
Affiliation:
University of Washington
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In the previous paper [7], we have studied the relationship between the Riemannian connection of an n-dimensional Riemannian space M imbedded into the (n + k)-dimensional Euclidean space Rn+k and the canonical connection in the bundle Pn, k = O(n + k)/{l} Х O(k) over the Grassmann manifold Mn, k = O(n + k)/O(n) Х O(k).

In the first half of the present paper, the relationship between the canonical connections in bundles and the invariant Riemannian connection on Mn, k will be discussed. We obtain the holonomy groups of these canonical connections.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 11 , February 1957 , pp. 93 - 109
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

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