Fixed-point theorems for groups acting on non-positively curved manifolds

Abstract

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.