Some Applications of the Hodge-de Rham Decomposition to Ricci Solitons |
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Authors: | C Aquino A Barros E Ribeiro Jr |
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Institution: | 1. Departamento de Matem??tica, UFC, 60455-760, Fortaleza, CE, Brazil
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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. |
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