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math.DG2022
On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons
Xu Cheng, Ernani Ribeiro, Detang Zhou
In this article, we investigate the geometry of -dimensional compact gradient Ricci solitons. We prove that, under an upper bound condition on the range of the potential functio…
math.DG2022
Hopf type theorems in Riemannian manifolds
Hilário Alencar, Gregório Silva Neto, Detang Zhou
In 1951, H. Hopf proved that the only surfaces, homeomorphic to the sphere, with constant mean curvature in the Euclidean space are the round (geometrical) spheres. In this paper w…