  We study vacua, walls and three-pronged junctions of mass-deformed nonlinear
sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ for generic $N$. We review and
discuss the on-shell component Lagrangians of the ${\mathcal{N}}=2$ nonlinear
sigma model on the Grassmann manifold, which are obtained in the
${\mathcal{N}}=1$ superspace formalism and in the harmonic superspace
formalism. We also show that the K\"{a}hler potential of the ${\mathcal{N}}=2$
nonlinear sigma model on the complex projective space, which is obtained in the
projective superspace formalism, is equivalent to the K\"{a}hler potential of
the ${\mathcal{N}}=2$ nonlinear sigma model with the Fayet-Iliopoulos
parameters $c^a=(0,0,c=1)$ on the complex projective space, which is obtained
in the ${\mathcal{N}}=1$ superspace formalism.
