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

By G. Catino, Carlo Mantegazza, L. Mazzieri. 2011

82 citations recorded by the source corpus.

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 space ℝn or to the round sphere 𝕊n. In particular, we show that any complete, noncompact, gradient Yamabe-type soliton with positive Ricci tensor is rotationally symmetric, whenever the potential function is nonconstant.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4c8b5a2db12f8b42b387bdd8434f31dc7029010a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. G. Catino
2. M. Rigoli
3. P. Mastrolia
4. D. Monticelli
5. E. Ribeiro
6. A. Barros
7. Xiuxiong Chen
8. Yuanqi Wang

In Astronomy and Astrophysics

1. G. Catino
2. M. Rigoli
3. D. Monticelli
4. P. Mastrolia
5. E. Ribeiro
6. A. Barros
7. Xiuxiong Chen
8. Yuanqi Wang

In Geometry and Topology

1. M. Rigoli
2. D. Monticelli
3. P. Mastrolia
4. G. Catino
5. Xiuxiong Chen
6. Yuanqi Wang

Citations in the corpus

• On the geometry of gradient einstein-type manifolds (2014, methodology): “This result covers the cases of Yamabe solitons [9] and conformal gradient solitons [15].”