Addendum to: ``Almost Ricci solitons and \(K\)-contact geometry'' (Q824303)

Ricci solitons arise as limits of the Ricci flow in some cases (and likewise Kähler-Ricci solitons). Sasakian manifolds are in some sense, odd-dimensional version of Kähler manifolds. Akin to the Kähler-Einstein condition, it is of interest to study Saskian-Einstein manifolds. In this context, an earlier result of the author [Monatsh. Math. 175, No. 4, 621--628 (2014; Zbl 1307.53038)] was ``A complete Ricci soliton whose metric $g$ is $K$-contact and the soliton vector field $X$ is strictly contact, is compact Sasakian Einstein''. In this addendum, this result is improved to ``a complete Ricci soliton \((M, g,X)\) whose metric \(g\) is a contact metric and the soliton vector field \(X\) is strictly contact, then \(X\) is an infinitesimal automorphism and \(g\) is Einstein'' (Theorem 1). Moreover, he proves in Proposition 1 that if a Ricci soliton \((M, g,X)\) has \(X\) as the Reeb vector field \(\xi\) of a contact metric structure on \((M,g)\), then \((M,g)\) is compact Einstein and Sasakian.