Mathematics
Generalizations of Kähler-Ricci solitons on projective bundles
Document Type
Article
Abstract
We prove that an admissible manifold (as defined by Apostolov, Calderbank, Gauduchon and Toønnesen-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 metric type, defined by the requirement that the scalar curvature isan affine combination of a Killing potential and its Laplacian.
Publication Title
Mathematica Scandinavica
Publication Date
2011
Volume
108
Issue
2
First Page
161
Last Page
176
ISSN
0025-5521
DOI
10.7146/math.scand.a-15165
Keywords
Kähler-Ricci solitons
Repository Citation
Maschler, Gideon and Toønnesen-Friedman, Christina W., "Generalizations of Kähler-Ricci solitons on projective bundles" (2011). Mathematics. 38.
https://commons.clarku.edu/mathematics/38
