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Connections Satisfying a Generalized Ricci Lemma
Published online by Cambridge University Press: 20 November 2018
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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
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- Copyright © Canadian Mathematical Society 1964
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