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Publications Influence

Generalized quasi-Einstein manifolds with harmonic Weyl tensor

- G. Catino
- Mathematics
- 24 December 2010

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 a… Expand

74 8- PDF

ON THE GLOBAL STRUCTURE OF CONFORMAL GRADIENT SOLITONS WITH NONNEGATIVE RICCI TENSOR

- G. Catino, C. Mantegazza, L. Mazzieri
- Mathematics
- 1 September 2011

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 Euclidean… Expand

28 5- PDF

Integral pinched shrinking Ricci solitons

- G. Catino
- Mathematics
- 24 September 2015

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 $\mathbb{S}^{n}$. The… Expand

30 5- PDF

Evolution of the Weyl Tensor under the Ricci Flow

- G. Catino, C. Mantegazza
- Mathematics
- 25 October 2009

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.

54 4- PDF

Bach-flat gradient steady Ricci solitons

- H. Cao, G. Catino, Q. Chen, C. Mantegazza, L. Mazzieri
- Mathematics
- 22 July 2011

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 a… Expand

60 3- PDF

Complete gradient shrinking Ricci solitons with pinched curvature

- G. Catino
- Mathematics
- 31 March 2011

We prove that any n-dimensional complete gradient shrinking Ricci soliton with pinched Weyl curvature is a finite quotient of $${\mathbb{R}^{n}, \mathbb{R}\times \mathbb{S}^{n-1}}$$ or… Expand

24 3- PDF

On the geometry of gradient einstein-type manifolds

- G. Catino, P. Mastrolia, D. Monticelli, M. Rigoli
- Mathematics
- 14 February 2014

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 Ricci… Expand

25 2- PDF

Some rigidity results on critical metrics for quadratic functionals

- G. Catino
- Mathematics
- 2 April 2014

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. It… Expand

17 2- PDF

Classification of expanding and steady Ricci solitons with integral curvature decay

- G. Catino, P. Mastrolia, D. Monticelli
- Mathematics
- 7 January 2015

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 scalar… Expand

16 2- PDF

Gradient Ricci solitons with vanishing conditions on Weyl

- G. Catino, P. Mastrolia, D. Monticelli
- Mathematics
- 1 February 2016

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 $n$-dimensional… Expand

22 2- PDF