A note on Kazdan-Warner-type identities

Article
  • 158 Downloads

Abstract

In this article we deal with f-conformal Killing vector fields, a generalization of conformal Killing vector fields involving a function f and two real parameters. Under certain conditions on f and the parameters, some non-existence results for such vector fields are proven. Moreover we derive a generalization of the Kazdan-Warner and Bourguignon-Ezin identities to the case of f-conformal Killing vector fields. Based on these, finally we present an application to the f-conformal solitons, a generalization of the Yamabe solitons.

Keywords

Kazdan-Warner-type identity Conformal Killing vector field Soliton 

Mathematics Subject Classification (2000)

38G25 35P05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Peter, P.: Riemannian Geometry. Graduate Texts in Mathematics, vol. 171. Springer, New York (1998) Google Scholar
  2. 2.
    Chow, B., Lu, P., Ni, L.: Hamilton’s Ricci Flow. Lectures in Contemporary Mathematics, vol. 3, Science Press and Graduate Studies in Mathematics, vol. 77. American Mathematical Society (co-publication) (2006) Google Scholar
  3. 3.
    Kazdan, J.L., Warner, F.W.: Curvature functions for compact 2-manifolds. Ann. Math. 99(2), 14–47 (1974) MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bourguignon, J.P., Ezin, J.P.: Scalar curvature functions in a conformal class of metrics and conformal transformations. Trans. Am. Math. Soc. 301(2), 723–736 (1987) MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Mathematisches Seminar der Universität Hamburg and Springer 2011

Authors and Affiliations

  1. 1.Department of MathematicsEast China Normal UniversityShanghaiPeople’s Republic of China

Personalised recommendations