  Based on $16,283$ early-type galaxies (ETGs) in $0.025\le
z_\mathrm{spec}<0.055$ from Sloan Digital Sky Survey data, we show that the
fundamental plane (FP) of ETGs is not a plane in the strict sense but is a
curved surface with a twisted shape whose orthogonal direction to the surface
is shifted as the central velocity dispersion ($\sigma_0$) or mean surface
brightness within the half-light radius ($\mu_e$) changes. When ETGs are
divided into subsamples according to $\sigma_0$, the coefficient of $\mu_e$ of
the FP increases, whereas the zero-point of the FP decreases at higher
$\sigma_0$. Taking the $z$ band as an example, the coefficient of $\mu_e$ rises
from $0.28$ to $0.36$ as $\sigma_0$ increases from $\sim100$ to $\sim300$ km
s$^{-1}$. At the same time, the zero-point of the FP falls from $-7.5$ to
$-9.0$ in the same $\sigma_0$ range. The consistent picture on the curved
nature of the FP is also reached by inspecting changes in the FP coefficients
for ETG subsamples with different $\mu_e$. By examining scaling relations that
are projections of the FP, we suggest that the warped nature of the FP may
originate from dry merger effects that are imprinted more prominently in ETGs
with higher masses.
