Abstract
In this paper, we discuss Calabi’s equation of the Kahler–Ricci soliton type on a compact Kahler manifold. This equation was introduced by Zhu as a generalization of Calabi’s conjecture. We give necessary and sufficient conditions for the unique existence of a solution for this equation on a compact Kahler manifold with a holomorphic vector field which has a zero point. We also consider the case of a nowhere vanishing holomorphic vector field, and give sufficient conditions for the unique existence of a solution for this equation.
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