Abstract
We construct 1-parameter families of well known solutions to the Yamabe problem defined on maximal flag manifolds to determine bifurcation instants for these families looking at changes of the Morse index of these metrics when the parameter varies on the interval [0,1]. A bifurcation point for such families is an accumulation point of others solutions to the Yamabe problem and a local rigidity point is a isolated solution of this problem, i.e., is not a bifurcation point.
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