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Local rigidity of certain actions of solvable groups on the boundaries of rank-one symmetric spaces

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  • Let $ G $ be the group of orientation-preserving isometries of a rank-one symmetric space $ X $ of non-compact type. We study local rigidity of certain actions of a solvable subgroup $ \Gamma \subset G $ on the boundary of $ X $, which is diffeomorphic to a sphere. When $ X $ is a quaternionic hyperbolic space or the Cayley hyperplane, the action we constructed is locally rigid.

    Mathematics Subject Classification: Primary: 37C85; Secondary: 53C24, 57S30.

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