Let $G$ be a linear connected semisimple Lie group, $\mathfrak g$ its Lie algebra. With respect to the Cartan involution $$ \theta:X\mapsto -\overline{X}^t, $$ one has $\mathfrak{g}=\mathfrak{k}\oplus \mathfrak{p}$.
Let $\mathfrak{a}$ be a maximal abelian subspace of $\mathfrak p$, $\mathfrak{t}$ a maximal abelian subspace of $\mathfrak{m}=C_\mathfrak{k}(\mathfrak a)$. Then $$\mathfrak{h}_r=\mathfrak{a}\oplus \mathfrak{t}$$ is a $\theta$-stable Cartan subalgebra with maxinum real rank.
Let $\mathfrak{t_0}$ be a maximal abelian subspace of $\mathfrak k$. Then $$\mathfrak h_1=C_\mathfrak{g}(\mathfrak{t}_0)=\mathfrak t_0\oplus C_\mathfrak{p}(\mathfrak{t}_0)$$ is the $\theta$-stable Cartan subalgebra with minumun real rank.
How to classify other $\theta$-stabl Cartan subalgebras?