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We prove that there exists at least one positive Einstein metric on$\mathbb{HP}^{m+1}\sharp \overline{\mathbb{HP}}^{m+1}$ for $m\geq 2$. Based onthe existence of the first Einstein metric, we give a criterion to check theexistence of a second Einstein metric on $\mathbb{HP}^{m+1}\sharp\overline{\mathbb{HP}}^{m+1}$. We also investigate the existence ofcohomogeneity one positive Einstein metrics on $\mathbb{S}^{4m+4}$ and provethe existence of a non-standard Einstein metric on $\mathbb{S}^8$.

Positive Einstein Metrics with $\mathbb{S}^{4m+3}$ as Principal Orbit