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Existence of Linear Connections with Respect to Which Given Tensor Fields are Parallel or Recurrent

Published online by Cambridge University Press:  22 January 2016

Yung-Chow Wong
Yung-Chow Wong*
Affiliation:
University of Hong Kong, Hong Kong
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Let M be an n-dimensional (n≥2) connected C∞-manifold with a linear connection. For simplicity, tensor fields on M will simply be called tensors on M. A tensor S on M is said to be parallel if its covariant derivative is everywhere zero in M, i.e., if ▽S = 0. S is said to be recurrent if its covariant derivative is equal to the tensor product of a covector and S itself, i.e., if ▽S = W⊗S, where W is called the recurrence covector.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 24 , June 1964 , pp. 67 - 108
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1964

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