
In the present paper, the authors study generalized Ricci solitons in the framework of paracontact metric manifolds. It is interesting that the equation for a metric \(g\) to be a generalized Ricci soliton unifies various important equations such as: homothetic vector field, Killing vector field, Ricci soliton, metric projective structure equation in the projective class for which the Ricci tensor is skew-symmetric, the equation of vacuum near horizon geometry, the equation of Einstein-Weyl. In the first result of the paper, under assumptions, the authors obtain \(K\)-paracontact and \(\eta\)-Einstein manifolds, whenever they start with a paracontact metric manifold. In the second important result they assume conditions on the \(K\)-paracontact metric to obtain a Einstein metric. In the third main result of the work, the authors assume that the K-paracontact metric is a gradient generalized almost Ricci soliton and they obtain conditions on the scalar curvature and on the squared norm of the Ricci operator. Finally they compute some explicit examples.
Special Riemannian manifolds (Einstein, Sasakian, etc.), paracontact metric manifold, General geometric structures on manifolds (almost complex, almost product structures, etc.), para-Sasakian manifold, \(K\)-paracontact manifold, Almost contact and almost symplectic manifolds, generalized Ricci soliton
Special Riemannian manifolds (Einstein, Sasakian, etc.), paracontact metric manifold, General geometric structures on manifolds (almost complex, almost product structures, etc.), para-Sasakian manifold, \(K\)-paracontact manifold, Almost contact and almost symplectic manifolds, generalized Ricci soliton
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