In this paper, we prove that a compact quasi-Einstein manifold $(M^n,\,g,\,u)$ of dimension $n\geq 4$ with boundary $\partial M,$ nonnegative sectional curvature and zero radial Weyl tensor is either isometric, up to scaling, the standard hemisphere $\Bbb {S}^n_+,$ or $g=dt^{2}+\psi ^{2}(t)g_{L}$ $u=u(t),$ where $g_{L}$ Einstein Ricci curvature. A similar classification result obtained by assum...

We construct complete gradient Kähler–Ricci solitons of various types on the total spaces of certain holomorphic line bundles over compact Kähler–Einstein manifolds with positive scalar curvature. Those are noncompact analogues of the compact examples found by Koiso [On rotationally symmetric Hamilton’s equations for Kähler–Einstein metrics, in Recent Topics in Differential and Analytic Geometr...

Abstract In this paper, we classify the compact locally homogeneous non-gradient m -quasi Einstein 3- manifolds. Along way, also prove that given a quotient of Lie group any dimension is Einstein, potential vector field X must be left invariant and Killing. We nontrivial metrics are product two metrics. show S 1 only manifold which admits metric nontrivially Einstein.