Mathematical Research Letters

Volume 19 (2012)

Number 4

On the structure of gradient Yamabe solitons

Pages: 767 – 774

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n4.a3

Authors

Huai-Dong Cao (Department of Mathematics, Lehigh University, Bethlehem, Penn., U.S.A.)

Xiaofeng Sun (Department of Mathematics, Lehigh University, Bethlehem, Penn., U.S.A.)

Yingying Zhang (Department of Mathematics, Lehigh University, Bethlehem, Penn., U.S.A.)

Abstract

We show that every complete nontrivial gradient Yamabe soliton admits a special global warped product structure with a one-dimensional base. Based on this, we obtain a general classification theorem for complete nontrivial locally conformally flat gradient Yamabe solitons.

2010 Mathematics Subject Classification

53C25, 53C44

Full Text (PDF format)