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Results in Mathematics

, 60:245 | Cite as

Some Applications of the Hodge-de Rham Decomposition to Ricci Solitons

  • C. Aquino
  • A. BarrosEmail author
  • E. RibeiroJr.
Article

Abstract

The aim of this paper is to present a link between the Perelman potential for a compact Ricci soliton M n and the Hodge-de Rham decomposition theorem, we shall use this result to present an integral formula which enables us to establish conditions under which the Ricci soliton is trivial. Moreover, given a Ricci soliton such that its associated vector field X is a conformal vector field we show that in the compact case X is a Killing vector field, while for the non-compact case, either the soliton is Gaussian or X is a Killing vector field.

Mathematics Subject Classification (2010)

Primary 53C25 53C20 53C21 Secondary 53C65 

Keywords

Hodge-de Rham Ricci soliton conformal fields 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Departamento de MatemáticaUFCFortalezaBrazil

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