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${T}^{2} \times {S}^{3} $ and related manifolds
We prove the existence of extremal Sasakian structures occurring on a countably infinite number of distinct contact structures on 
${T}^{2} \times {S}^{3} $ and certain related 5-manifolds. These structures occur in bouquets and exhaust the Sasaki cones in all except one case in which there are no extremal metrics.
