Affine Yano and perturbed Yano–Ricci solitons on Lorentzian Lie groups

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Abstract

In this paper, we defined affine Yano–Ricci solitons and perturbed Yano–Ricci solitons on three-dimensional Lorentzian Lie groups and obtain their complete classification. The major results indicated that all groups G₃, · · · ,G₇ admit both affine Yano–Ricci solitons and their perturbed companions, whereas G₁ supports neither. As a corollary, we found that the Lorentzian Lie groups G₃,G₅, and G₆ are affine Einstein manifolds with respect to the Yano connection.

Keywords

affine Yano–Ricci solitons / affine perturbed Yano–Ricci solitons / Lorentzian Lie groups / affine Einstein manifold

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