Abstract
Here, it is shown a compact generalized quasi-Einstein or briefly a GQE manifold has the finite fundamental group. Next, under certain assumptions, a rigidity result shows that a compact GQE manifold is diffeomorphic to the standard n-sphere. As a corollary, if the scalar curvature is constant, then it is isometric to the standard n-sphere. Meanwhile, a trivialization criterion and existence of harmonic vector fields on a GQE are studied.
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