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

Results in Mathematics - Tập 60 - Trang 245-254 - 2011
C. Aquino1, A. Barros1, E. Ribeiro1
1Departamento de Matemática, UFC, Fortaleza, Brazil

Tóm tắt

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.

Tài liệu tham khảo

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