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Integration of Subspaces Derived from a Linear Transformation Field

Published online by Cambridge University Press:  20 November 2018

Edward T. Kobayashi
Edward T. Kobayashi*
Affiliation:
University of Washington
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The problem we study is a generalization of a problem first solved by Tonolo (6), then generalized successively by Schouten (5), Nijenhuis (4), Haantjes (3), and Nijenhuis-Frölicher (2). The Tonolo- Schouten approach is distinct from that of Nijenhuis-Haantjes-Frölicher in the sense that the former consider the problem on a Riemannian space, while the latter consider it on a manifold without any further structure.

The object of investigation is the integrability of the distribution θ of vector subspaces θP of the tangent space Tp to a manifold M, when θP is intrinsically related to a given field h on M, of linear transformations hp on Tv. The research has so far been restricted to certain types of h.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 273 - 282
Copyright
Copyright © Canadian Mathematical Society 1961

References

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