  This is a continuous work about the nonexistence of some complete metrics on
the product of two manifolds studied by Tam-Yu [Asian Journal of Mathematics,
14(2010)]. Motivated by the result of Tossati [Comm.Anal.Geom. 15(2007)]. We
generalize the corresponding results of Tam-Yu [Asian Journal of Mathematics,
14(2010)] to the almost-Hermitian case.
