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Self-consistent axially symmetric Skyrme Hartree-Fock plus BCS calculationsare performed to study the evolution of shapes with the number of nucleons invarious chains of Yb, Hf, W, Os, and Pt isotopes from neutron number N=110 upto N=122. Potential energy curves are analyzed in a search for signatures ofoblate-prolate phase shape transitions and results from various Skyrme andpairing forces are considered. Comparisons with results obtained with the Gognyinteraction as well as with relativistic mean field calculations are presented.The role of the $\gamma$ degree of freedom is also discussed.

Shape transitions in neutron-rich Yb, Hf, W, Os, and Pt isotopes within a Skyrme Hartree-Fock + BCS approach