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 the soliton is a steady tracelessκ-Einstein soliton and is realized on the cotangent bundle of an affine surface.
Departamento de Matemáticas, Escola Politécnica Superior , Universidade da Coruña , Coruña, Spain.
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M
Brozos-Vázquez
Faculty of Mathematics , University of Santiago de Compostela , 15782 Santiago de Compostela, Spain.
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0000-0003-1195-1664
E
García-Río
Faculty of Mathematics , University of Santiago de Compostela , 15782 Santiago de Compostela, Spain.
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X
Valle-Regueiro
Walker manifold; gradient Ricci almost soliton; half conformally flat; warped product