Vol. 286, No. 2, 2017

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ISSN: 0030-8730
Conformally Kähler Ricci solitons and base metrics for warped product Ricci solitons

Gideon Maschler

Vol. 286 (2017), No. 2, 361–384
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.

Keywords
Ricci soliton, quasi-soliton, quasi-Einstein, Kähler, conformal, warped product
Mathematical Subject Classification 2010
Primary: 53C25
Secondary: 53C55, 53B35
Milestones
Received: 30 April 2015
Revised: 6 February 2016
Accepted: 22 July 2016
Published: 15 January 2017
Authors
Gideon Maschler
Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610-1477
United States