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In this article, we classify totally geodesic submanifolds in arbitrary products of rank one symmetric spaces.Furthermore, we give infinitely many examples of irreducible totally geodesic submanifolds in Hermitian symmetric spaces with non-trivial constant Kähler angle, i.e. they are neither complex nor totally real.
Alberto Rodríguez Vázquez Rodríguez Vázquez (Mon,) studied this question.