Isometry Groups of Some Dunwoody Manifolds

Dunwoody manifolds are an interesting class of closed connected orientable 3--manifolds, which are defined by means of Heegaard diagrams having a rotational symmetry. They are proved to be cyclic coverings of lens spaces (possibly S^3) branched over (1,1)--knots. Here we study the Dunwoody manifolds which are cyclic coverings of the 3--sphere branched over two specified families of Montesinos knots. Then we determine the Dunwoody parameters for such knots and the isometry groups for the considered manifolds in the hyperbolic case. A list of volumes for some hyperbolic Dunwoody manifolds completes the paper.