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Generalized quasi-Einstein manifolds with harmonic Weyl tensor
In this paper we introduce the notion of generalized quasi-Einstein manifold that generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi-Einstein manifolds. We prove that aExpand
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ON THE GLOBAL STRUCTURE OF CONFORMAL GRADIENT SOLITONS WITH NONNEGATIVE RICCI TENSOR
In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product ℝ × Nn-1, or globally conformally equivalent to the EuclideanExpand
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Integral pinched shrinking Ricci solitons
We prove that a $n$-dimensional, $4 \leq n \leq 6$, compact gradient shrinking Ricci soliton satisfying a $L^{n/2}$-pinching condition is isometric to a quotient of the round $\mathbb{S}^{n}$. TheExpand
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Evolution of the Weyl Tensor under the Ricci Flow
We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons.
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Bach-flat gradient steady Ricci solitons
In this paper we prove that any n-dimensional (n ≥ 4) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that aExpand
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Complete gradient shrinking Ricci solitons with pinched curvature
We prove that any n-dimensional complete gradient shrinking Ricci soliton with pinched Weyl curvature is a finite quotient of $${\mathbb{R}^{n}, \mathbb{R}\times \mathbb{S}^{n-1}}$$ orExpand
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On the geometry of gradient einstein-type manifolds
In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold $\varrg$, unifying various particular cases recently studied in the literature, such as gradient RicciExpand
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Some rigidity results on critical metrics for quadratic functionals
In this paper we prove rigidity results on critical metrics for quadratic curvature functionals, involving the Ricci and the scalar curvature, on the space of Riemannian metrics with unit volume. ItExpand
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Classification of expanding and steady Ricci solitons with integral curvature decay
In this paper we prove new classification results for nonnegatively curved gradient expanding and steady Ricci solitons in dimension three and above, under suitable integral assumptions on the scalarExpand
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Gradient Ricci solitons with vanishing conditions on Weyl
We classify complete gradient Ricci solitons satisfying a fourth-order vanishing condition on the Weyl tensor, improving previously known results. More precisely, we show that any $n$-dimensionalExpand
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