The classification of locally conformally flat Yamabe solitons

By Daskalopoulos Panagiota, N. Šešum. 2011

162 citations recorded by the source corpus.

We provide the classification of locally conformally flat gradient Yamabe solitons with positive sectional curvature. We first show that locally conformally flat gradient Yamabe solitons with positive sectional curvature have to be rotationally symmetric and then give the classification and asymptotic behavior of all radially symmetric gradient Yamabe solitons. We also show that any eternal solutions to the Yamabe flow with positive Ricci curvature and with the scalar curvature attaining an interior space-time maximum must be a steady Yamabe soliton.

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

View Paper: https://www.semanticscholar.org/paper/df141d6a296ff8f8a6fa8efacfc97a80648ed44b

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, background): “Other examples are, for instance, Ricci almost solitons ([41]), Yamabe solitons ([19], [31],[21], [9]), Yamabe quasi-solitons ([27], [45]), conformal gradient solitons ([43], [15]), quasi-Einstein manifolds ([30], [12], [16], [26], [35]), ρ-Einstein solitons ([17], [18]).”