A note on locally conformally flat gradient Ricci solitons

We show that locally conformally flat gradient Ricci solitons, possibly incomplete, are locally isometric to a warped product of an interval and a space form. Consequently, we get that complete gradient shrinking and steady Ricci solitons with vanishing Weyl tensor are rotationally symmetric, from w...

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Bibliographic Details
Published inGeometriae dedicata Vol. 168; no. 1; pp. 1 - 7
Main Authors Fernández-López, Manuel, García-Río, Eduardo
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.02.2014
Subjects
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
Warped product
Gradient Ricci soliton
Conformally flat
53C25
Weyl tensor
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Summary:We show that locally conformally flat gradient Ricci solitons, possibly incomplete, are locally isometric to a warped product of an interval and a space form. Consequently, we get that complete gradient shrinking and steady Ricci solitons with vanishing Weyl tensor are rotationally symmetric, from which their classification follows.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-012-9815-0