Half conformally flat gradient Ricci almost solitons

Half conformally flat gradient Ricci almost solitons

The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighbourhood of any point where the gradient of the potential function is non-null. In opposition, if the gradient of the potential function is null, then...

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Veröffentlicht in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2016-05, Vol.472 (2189), p.20160043-20160043
Hauptverfasser: Brozos-Vázquez, M., García-Río, E., Valle-Regueiro, X.
Format: Artikel
Sprache:eng
Schlagworte:
Gradient Ricci Almost Soliton
Half Conformally Flat
Walker Manifold
Warped Product
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Zusammenfassung:The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighbourhood of any point where the gradient of the potential function is non-null. In opposition, if the gradient of the potential function is null, then the soliton is a steady traceless κ-Einstein soliton and is realized on the cotangent bundle of an affine surface.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2016.0043