Positive Einstein metrics with as the principal orbit

We prove that there exists at least one positive Einstein metric on HP^m+1 {HP}^m+1 for m ~2. Based on the existence of the first Einstein metric, we give a criterion to check the existence of a second Einstein metric on HP^m+1 {HP}^m+1. We also investigate the existence of cohomogeneity-one positive Einstein metrics on S^4m+4 and prove the existence of a non-standard Einstein metric on S⁸.