A geometric proof of the Matsuki orbit duality for flag manifolds is established in [R. Bremigan and J. Lorch, Orbit duality for flag manifolds, Manuscripta Math. 109 (2002), 233-261.] by analyzing the gradient flow of the norm-squared of a moment map. In the present paper, we investigate explicit formulas for integral curves associated with this flow, leading to a correspondence between certain integral curves and Cayley transforms. In addition, an exhaustive collection of curves is presented in the rank-one hermitian symmetric case.
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