Osaka Journal of Mathematics

On generalized Kähler--Ricci solitons

Yasuhiro Nakagawa

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Abstract

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

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

Dates
First available in Project Euclid: 6 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1315318350

Mathematical Reviews number (MathSciNet)
MR2831983

Zentralblatt MATH identifier
1234.32006

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

Citation

Nakagawa, Yasuhiro. On generalized Kähler--Ricci solitons. Osaka J. Math. 48 (2011), no. 2, 497--513. https://projecteuclid.org/euclid.ojm/1315318350


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