Recurrent tensor

definition

Let ${\displaystyle \nabla }$  be a connection on the manifold M. A tensor T called recurrent with respect to ${\displaystyle \nabla }$ , iff there is a one-form ${\displaystyle \omega }$  on M, such that

${\displaystyle \nabla T=\omega \otimes T}$ 

example

An example for a recurrent tensor is a Weyl structure on M.