Kähler gradient Ricci solitons with large symmetry

Let (M, g, J, f) be an irreducible non-trivial K & auml;hler gradient Ricci soliton of real dimension 2n. We show that its group of isometries is of dimension at most n2 and the case of equality is characterized. As a consequence, our framework shows the uniqueness of U(n)-invariant K & auml;hler gradient Ricci solitons constructed earlier. There are corollaries regarding the groups of automorphisms or affine transformations and a general version for almost Hermitian GRS. The approach is based on a connection to the geometry of an almost contact metric structure. Published by Elsevier Inc.