Irregular Eguchi–Hanson type metrics and their soliton analogues

We verify the extension to zero section of momentum construction Kaehler-Einstein metrics and Kaehler-Ricci solitons on total space Y positive rational powers canonical line bundle toric Fano manifolds with possibly irregular Sasaki-Einstein metrics. More precisely, we show that extended metric along has an expression which can be Y, restricts associated unit circle as a transversely (Sasakian eta-Einstein) scaled in Reeb flow direction, there is Riemannian submersion from Sasakian eta-Einstein induced section.