We present a series of recent works on the gravitational
form factors (GFFs) of the nucleon within a pion mean-field
approach, which is also called the chiral quark-soliton model. We
investigate the flavor structure of the mass, angular momentum,
and $D$-term form factors of the nucleon. The main findings of the
present work are given as follows: the contribution of the strange
quark is rather small for the mass and angular momentum form
factors, it plays an essential role in the $D$-term form factors. It
indicates that the $D$-term form factor is sensitive to the outer
part of the nucleon. The flavor blindness, i.e, $D^{u-d}\simeq 0$,
is valid only if the strange quark is considered.
We also discuss the effects of twist-4 operators. Though the gluonic
contributions are suppressed by the packing fraction of the
instanton vacuum in the twist-2 case, contributions from twist-4
operators are significant.