Classification of almost Yamabe solitons in Euclidean spaces

Study on Twisted Product Almost Gradient Yamabe Solitons

“…In [9], they found sufficient conditions on the soliton vector field under which the metric of a Yamabe soliton is a Yamabe metric, that is, a metric of constant scalar curvature. Moreover, in [8], we can see the various examples of compact and noncompact almost gradient Yamabe soliton. e present authors [4] studied gradient Yamabe soliton in the warped product manifolds and admittance of gradient Yamabe solitons and geometric structures for some model spaces.…”

“…[2 -7]. In (2), if ρ is a function on M, then M is called an almost gradient Yamabe soliton with (h, ρ) [8]. e Yamabe soliton (resp., gradient Yamabe soliton) is said to be trivial if X is killing (resp., h is a constant).…”

“…Especially considering the condition of the conformal flatness, the classification and characterizations of the space were greatly helped. In addition to these, there are many works on solitons on the twisted product spaces [10][11][12][13][14] and Yamabe solitons [2,[5][6][7][8][9].…”

Geometry of k-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields

“…More triviality results can be found in [3], that is, every compact gradient k-Yamabe soliton must have constant k-curvature and certain conditions over the gradient. On the other hand, Yamabe solitons and quasi-Yamabe solitons with concurrent vector fields are discussed in [6] and also in a great number of good results in [7][8][9][10][11][12][13][14][15][16][17][18]. Motivated by some previous results regarding the classification of the theory of solitons geometry; we shall study some geometric classifications notes for k-Yamabe solitons on Euclidean hypersurfaces, if it is a potential field, originated from their position vector fields.…”

Some remarks on Riemannian submersions admitting an almost Yamabe soliton

“…Yamabe solitons are self-similar solutions for Yamabe flows and they seem to be as singularity models. More clearly, the Yamabe soliton comes from the blow-up procedure along the Yamabe flow, so such solitons have been studied intensively (see [2][3][4][5][6][7][8]).…”