Abstract
The concept of C^h- recurrent Finsler space has been studied by M.Matsumoto [6] . H.Izumi ([4],[5]) gave the concept of *P- spaces which was the generalization of C^h-recurrent spaces and P2-like spaces of M.Matsumoto ([6],[7]). R.Verma [15] discussed C^h- birecurrent spaces where these spaces are generalization of C^h- recurrent spaces of M.Matsumoto [6] .Besides the correlation of C^h- birecurrent spaces which C^h- recurrent space , some special C^h- birecurrent spaces has been discussed . The result concerning h- isotropic C^h- recurrent space due to M.Matsumoto [6] has been extended to C^h- birecurrent spaces by P.N. Pandey and R.Verma [15]. C.K.Mishra and G.Lodhi [9] studied the properties of C^h- recurrent and C^v- recurrent for torsion tensor field of the second order in Finsler spaces . 
 The purpose of the present paper is to study the properties of C^h- trirecurrent torsion tensor field and the recurrence covariant vector field of the third order in Finsler spaces .
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