Abstract: The author considered the Eisenhart problem of symmetric parallel (0,2)-type tensor fields with respect to a quarter-symmetric metric connection  by using tensor analysis method and Kenmotsu manifold’s structural equations. Under suitable conditions, the author  proved that the  tensor field must be a constant multiple of the metric tensor, and gave a necessary and sufficient condition for a Ricci symmetric Kenmotsu manifold to be an Einstein manifold.

Key words: quarter-symmetric metric connection, Kenmotsu manifold, Eisenhart problem