We investigate preheating of an inflaton field phi coupled nonminimally to
a spacetime curvature by the method of Hartree approximations. In the case
of a self-coupling inflaton potential V(phi) = lambda phi(4)/4, the dynamic
s of preheating changes by the effect of the negative xi. We find that the
nonminimal coupling works in two ways. First, since the initial value of th
e inflaton field for reheating becomes smaller with the increase of \xi\, t
he evolution of the inflaton quanta is delayed for fixed lambda. Second, th
e oscillation of the inflaton field is modified and the nonadiabatic change
around phi = 0 occurs significantly. That makes the resonant band of the f
luctuation field wider. Especially for strong coupling regimes \xi\ much gr
eater than 1, the growth of the inflaton fluctuation is dominated by the re
sonance due to the nonminimal coupling, which leads to a significant enhanc
ement of low momentum modes. Although the final variance of the inflaton fl
uctuation does not change significantly compared with the minimally coupled
case, we have found that the energy transfer from the homogeneous inflaton
to created particles efficiently occurs for xi less than or similar to - 6
0.