2011
DOI: 10.7146/math.scand.a-15165
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Generalizations of Kähler-Ricci solitons on projective bundles

Abstract: We prove that an admissible manifold (as defined by Apostolov, Calderbank, Gauduchon and Tønnesen-Friedman), arising from a base with a local Kähler product of constant scalar curvature metrics, admits Generalized Quasi-Einstein Kähler metrics (as defined by D. Guan) in all "sufficiently small" admissible Kähler classes. We give an example where the existence of Generalized Quasi-Einstein metrics fails in some Kähler classes while not in others. We also prove an analogous existence theorem for an additional me… Show more

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Cited by 9 publications
(9 citation statements)
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“…The above theorem agrees with Maschler-Tønnesen's result [MT11], which says that there exists a unique admissible GQE metric if the admissible data of Ω is sufficiently small. Now we describe the content of this paper.…”
Section: Introductionsupporting
confidence: 87%
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“…The above theorem agrees with Maschler-Tønnesen's result [MT11], which says that there exists a unique admissible GQE metric if the admissible data of Ω is sufficiently small. Now we describe the content of this paper.…”
Section: Introductionsupporting
confidence: 87%
“…In Section 3, we review the fundamental materials about admissible bundles [ACGT08] and define some notations that we will use later. In Section 4, we relate Maschler-Tønnesen's invariant [MT11] to Tian-Zhu's invariant [TZ02] on admissible bundles (cf. Theorem 4.2).…”
Section: Introductionmentioning
confidence: 99%
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“…It is shown in [5,47] that (40) gives rise to the eigenspace decomposition of the generator A k for the action of α on H 0 (M 0 , L k 0 ) as follows: each summand of on the first line corresponds to the eigenvalue 0 whereas (with the normalization (33) for A k ) the summands on the second line correspond to eigenvalues j. In the above equalities, ν * ∞ denotes the dual of the normal bundle of e ∞ .…”
Section: The Proof Of [5 Cor 3] Yieldsmentioning
confidence: 99%