The aim of this paper is to prove that a gradient almost Ricci soliton \({(M^{n}, g, \nabla f, \lambda )}\) whose Ricci tensor is Codazzi has constant sectional curvature. In particular, in the compact case, we deduce that (Mn, g) is isometric to a Euclidean sphere and f is a height function. Moreover, we also classify gradient almost Ricci solitons with constant scalar curvature R provided a suitable function achieves a maximum in Mn.

Integral formulas in riemannian geometry

A note on rigidity of the almost Ricci soliton

The aim of this paper is to present a link between the Perelman potential for a compact Ricci soliton Mn and the Hodge-de Rham decomposition theorem, we shall use this result to present an integral formula which enables us to establish conditions under which the Ricci soliton is trivial. Moreover, given a Ricci soliton such that its associated vector field X is a conformal vector field we show that in the compact case X is a Killing vector field, while for the non-compact case, either the soliton is Gaussian or X is a Killing vector field.

Some Applications of the Hodge-de Rham Decomposition to Ricci Solitons

A note on Ricci solitons

The object of this paper is to study Yamabe solitons on almost co-Kahler manifolds as well as on -almost co-Kahler manifolds.

Integral formulas in riemannian geometry

Citations

A note on rigidity of the almost Ricci soliton

Some Applications of the Hodge-de Rham Decomposition to Ricci Solitons

A note on Ricci solitons

Yamabe Solitons and Ricci Solitons on Almost co-Kähler Manifolds

On a differential equation characterizing Euclidean spheres

Related Papers (5)

Riemannian Geometry of Contact and Symplectic Manifolds

The entropy formula for the Ricci flow and its geometric applications

Certain conditions for a Riemannian manifold to be isometric with a sphere

A class of almost contact riemannian manifolds

Curvature and Betti numbers