Date: 16 Mar 2011

A note on Kazdan-Warner-type identities

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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.

Communicated by V. Cortés.