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The Weil-Petersson and VMOA Teichmuller spaces, subspaces of the universal Teichmuller space, are complex Banach manifolds modelled on different Banach spaces. We show that they are holomorphically contractible. It is given in (28) that the Kobayashi and Teichmul- ler metrics coincide with each other on the Weil-Petersson Teichmuller space. We show that this property is also true on the VMOA Teichmuller space. A couple of other properties of the two spaces are also obtained.

Holomorphic contractibility and other properties of the Weil-Petersson and VMOA Teichmüller spaces