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Let $ G $ be a connected reductive algebraic group over $ \C $. We denote by$ K = (G^{\theta})_{0} $ the identity component of the fixed points of aninvolutive automorphism $ \theta $ of $ G $. The pair $ (G, K) $ is called asymmetric pair.  Let $Q$ be a parabolic subgroup of $K$. We want to find a pair of parabolicsubgroups $P_{1}$, $P_{2}$ of $G$ such that (i) $P_{1} \cap P_{2} = Q$ and (ii)$P_{1} P_{2}$ is dense in $G$. The main result of this article states that, fora simple group $G$, we can find such a pair if and only if $(G, K)$ is aHermitian symmetric pair.  The conditions (i) and (ii) yield to conclude that the $K$-orbit through theorigin $(e P_{1}, e P_{2})$ of $G/P_{1} \times G/P_{2}$ is closed and itgenerates an open dense $G$-orbit on the product of partial flag variety. Fromthis point of view, we also give a complete classification of closed $K$-orbitson $G/P_{1} \times G/P_{2}$.

Closed orbits on partial flag varieties and double flag variety of finite type