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October, 2003 Rotationally Symmetric Shrinking and Expanding Gradient Kähler-Ricci Solitons
Mikhail Feldman, Tom Ilmanen, Dan Knopf
J. Differential Geom. 65(2): 169-209 (October, 2003). DOI: 10.4310/jdg/1090511686

Abstract

We construct new families of Kähler-Ricci solitons on complex line bundles over ℂℙn−1, n ≥ 2. Among these are examples whose initial or final condition is equal to a metric cone ℂn/ℤk. We exhibit a noncompact Ricci flow that shrinks smoothly and self-similarly for t < 0, becomes a cone at t = 0, and then expands smoothly and self-similarly for t > 0; this evolution is smooth in space-time except at a single point, at which there is a blowdown of a ℂℙn−1. We also construct certain shrinking solitons with orbifold point singularities.

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Mikhail Feldman. Tom Ilmanen. Dan Knopf. "Rotationally Symmetric Shrinking and Expanding Gradient Kähler-Ricci Solitons." J. Differential Geom. 65 (2) 169 - 209, October, 2003. https://doi.org/10.4310/jdg/1090511686

Information

Published: October, 2003
First available in Project Euclid: 22 July 2004

zbMATH: 1069.53036
MathSciNet: MR2058261
Digital Object Identifier: 10.4310/jdg/1090511686

Rights: Copyright © 2003 Lehigh University

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Vol.65 • No. 2 • October, 2003
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