GRADIENT RICCI SOLITONS WITH HALF HARMONIC WEYL CURVATURE AND TWO RICCI EIGENVALUES

초록

In this article we classify four dimensional gradient Ricci solitons (M, g, f) with half harmonicWeyl curvature and at most two distinct Ricci-eigenvalues at each point. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, (V, g) is isometric to one of the following: (i) an Einstein manifold. (ii) a domain in the Riemannian product (R2, g<inf>0</inf>) × (N, ~g), where g<inf>0</inf> is the at metric on R2 and (N, ~g) is a two dimensional Riemannian manifold of constant curvature λ ≠ 0. (iii) a domain in R×W with the warped product metric ds2 +h(s)2~g, where ~g is a constant curved metric on a three dimensional manifold W © 2022 Korean Mathematical Society

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