Mathematics
Conformally Kähler Ricci solitons and base metrics for warped product Ricci solitons
Document Type
Article
Abstract
We investigate Kähler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. A slight generalization of the latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton potential, with the conformal factor in the first case, and with the warping function in the second. The main result in the first case is a partial classification in dimension n ≥ 4. In the second case, Kähler quasi-soliton metrics satisfying the above main assumption are shown to be, under an additional genericity hypothesis, necessarily Riemannian products. Another theorem concerns quasi-soliton metrics satisfying the above main assumption, which are also conformally Kähler. With some additional assumptions it is shown that such metrics are necessarily base metrics of Einstein warped products, that is, quasi-Einstein.
Publication Title
Pacific Journal of Mathematics
Publication Date
2017
Volume
286
Issue
2
First Page
361
Last Page
384
ISSN
0030-8730
DOI
10.2140/pjm.2017.286.361
Keywords
conformal, Kähler, Quasi-Einstein, Quasi-soliton, Ricci soliton, warped product
Repository Citation
Maschler, Gideon, "Conformally Kähler Ricci solitons and base metrics for warped product Ricci solitons" (2017). Mathematics. 33.
https://commons.clarku.edu/mathematics/33
