Abstract
The purpose of this paper is to prove a Hitchin–Thorpe inequality for a four-dimensional compact almost Ricci soliton. Moreover, we prove that under a suitable integral condition, a four-dimensional compact almost Ricci soliton is isometric to standard sphere. Finally, we prove that under a simple condition, a four-dimensional compact Ricci soliton with harmonic self-dual part of Weyl tensor is either isometric to a standard sphere $$\mathbb S ^{4}$$ or is Kaehler–Einstein.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have