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We study isometric actions of Steinberg groups on Hadamard manifolds. We prove some rigidity properties related to these actions. In Particular we show that every isometric action of St n (F p t 1 , . . . , t k ) on Hadamard manifold when n ≥ 3 factors through a finite quotient.. We further study actions on infinite dimensional manifolds and prove a fixed point theorem related to such actions.Date: 17.12.15.