Rigidity of shrinking Ricci solitons

We show that a compact Ricci soliton is rigid if and only if the Weyl conformal tensor is harmonic. In the complete noncompact case we prove the same result assuming that the curvature tensor has at most exponential growth and the Ricci tensor is bounded from below.

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Bibliographische Detailangaben
Veröffentlicht in:	Mathematische Zeitschrift 2011-10, Vol.269 (1-2), p.461-466
Hauptverfasser:	Fernández-López, Manuel, García-Río, Eduardo
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We show that a compact Ricci soliton is rigid if and only if the Weyl conformal tensor is harmonic. In the complete noncompact case we prove the same result assuming that the curvature tensor has at most exponential growth and the Ricci tensor is bounded from below.
ISSN:	0025-5874 1432-1823
DOI:	10.1007/s00209-010-0745-y