Osaka Journal of Mathematics

On generalized Kähler--Ricci solitons

Yasuhiro Nakagawa

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By definition, Kähler--Ricci solitons are defined on Fano manifolds. In this note, we shall generalize the notion of Kähler--Ricci solitons to the case of general polarized manifolds from the view point of K-energy, which are called ``generalized Kähler--Ricci solitons''. Moreover, ``generalized Kähler--Ricci solitons'' are also one of generalizations of constant scalar curvature Kähler metrics. Furthermore, we shall give a non-trivial example of a ``generalized Kähler--Ricci soliton''.

Article information

Osaka J. Math., Volume 48, Number 2 (2011), 497-513.

First available in Project Euclid: 6 September 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx]
Secondary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)


Nakagawa, Yasuhiro. On generalized Kähler--Ricci solitons. Osaka J. Math. 48 (2011), no. 2, 497--513.

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