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Rigidity of gradient
Ricci solitons
Peter Petersen and William Wylie |
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Vol. 241 (2009), No. 2, 329–345
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Abstract |
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We define a gradient Ricci soliton to be rigid if it is a flat bundle N ×Γℝk where N is Einstein. It is known that not all gradient solitons are rigid. Here we offer several natural conditions on the curvature that characterize rigid gradient solitons. Other related results on rigidity of Ricci solitons are also explained in the last section. |
Keywords
complete manifold, constant scalar curvature, Ricci
soliton, Einstein manifold
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Mathematical Subject Classification 2000
Primary: 53C25
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Milestones
Received: 3 December 2008
Accepted: 15 December 2008
Published: 1 June 2009
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Authors |
| Peter Petersen | |
| Department of Mathematics University of California Los Angeles, CA 90095 United States |
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| http://www.math.ucla.edu/~petersen | |
| William Wylie | |
| Department of Mathematics University of Pennsylvania David Rittenhouse Lab 209 South 33rd Street Philadelphia, PA 19104 United States |
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| http://www.math.upenn.edu/~wylie | |
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