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Connections Satisfying a Generalized Ricci Lemma

Published online by Cambridge University Press:  20 November 2018

J. R. Vanstone
J. R. Vanstone*
Affiliation:
University of Toronto and Summer Research Institute of the Canadian Mathematical Congress
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In this paper we shall consider a generalization of a very old problem in differential geometry; namely, given a second-order covariant tensor field aij(x) on an n-dimensional manifold, when does there exist a connection such that the covariant derivative, defined by

vanishes?

The earliest question of this type arose in the case when is symmetric and positive definite. A solution connection of the problem is then given by the Christoffel symbols

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 549 - 560
Copyright
Copyright © Canadian Mathematical Society 1964

References

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3. Hlavaty, V., Geometry of Einstein's Unified Field Theory (Groningen, 1957).Google Scholar
4. Van der Waerden, B. L., Modern algebra, Vol. 1 (New York, 1949).Google Scholar