Ernani Ribeiro

Rigidity of four-dimensional compact manifolds with harmonic Weyl tensor

We prove that a 4-dimensional compact manifold

Characterizations and integral formulae for generalized m-quasi-Einstein metrics

M^4

A note on rigidity of the almost Ricci soliton

M4 with harmonic Weyl tensor must be either locally conformally flat or isometric to a complex projective space

Critical metrics of the total scalar curvature functional on 4-manifolds

\mathbb {CP}^2,

Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary

CP2, provided that the biorthogonal (sectional) curvature satisfies a suitable pinching condition. In particular, we improve the pinching constants considered by some preceding works on a rigidity result for 4-dimensional compact manifolds.