Classification of Gradient Ricci Solitons with Harmonic Weyl Curvature

초록

We make classifications of gradient Ricci solitons (M, g, f) with harmonic Weyl curvature. As a local classification, we show that the associated Riemannian metric g is locally among the types (i)-(iv) in Theorem 1. Compared with the previous four-dimensional study in [25], we have developed a novel method of refined adapted frame fields and overcome the main difficulty arising from a large number of Riemmannian connection components in dimension >= 5$\ge 5$. Next we have obtained a classification of complete ones with harmonic Weyl curvature. For the proof, using the real analytic nature of g and f, we elaborate geometric arguments to fit together local regions.

키워드