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Classification of
expanding and steady Ricci solitons with integral curvature
decay
Giovanni Catino, Paolo Mastrolia and Dario D Monticelli |
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Geometry & Topology 20 (2016) 2665–2685
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Abstract |
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In this paper we prove new classification results for nonnegatively curved gradient expanding and steady Ricci solitons in dimension three and above, under suitable integral assumptions on the scalar curvature of the underlying Riemannian manifold. In particular we show that the only complete expanding solitons with nonnegative sectional curvature and integrable scalar curvature are quotients of the Gaussian soliton, while in the steady case we prove rigidity results under sharp integral scalar curvature decay. As a corollary, we obtain that the only three-dimensional steady solitons with less than quadratic volume growth are quotients of or of , where is Hamilton’s cigar. |
Keywords
Ricci solitons, Weitzenböck formula, weighted Einstein
tensor, rigidity results
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Mathematical Subject Classification 2010
Primary: 53C20, 53C25
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References |
Publication
Received: 7 January 2015
Revised: 23 September 2015
Accepted: 9 November 2015
Published: 7 October 2016
Proposed: Gang Tian
Seconded: John Lott, Tobias H. Colding
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Authors |
| Giovanni Catino | |
| Dipartimento di Matematica Politecnico di Milano Piazza Leonardo da Vinci 32 I-20133 Milano Italy |
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| Paolo Mastrolia | |
| Dipartimento di Matematica Università Degli Studi di Milano Via Saldini 50 %deleted Cesare I-20133 Milano %paper had Milano, Italy 20133 Italy |
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| Dario D Monticelli | |
| Dipartimento di Matematica Politecnico di Milano Piazza Leonardo da Vinci 32 I-20133 Milano %paper had Milano, Italy 20133 Italy |
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