Related papers: On Warped Product Gradient Yamabe Solitons
In this paper, we consider generalized Yamabe solitons which include many notions, such as Yamabe solitons, almost Yamabe solitons, h-almost Yamabe solitons, gradient k-Yamabe solitons and conformal gradient solitons. We completely classify…
We study complete conformal gradient solitons, a class containing gradient Yamabe solitons and many generalized Yamabe-type structures, including gradient almost Yamabe, gradient k-Yamabe, and gradient h-almost Yamabe solitons, and, after a…
In this paper, we show that any compact quasi $k$-Yamabe gradient solitons must have constant $\sigma_{k}$-curvature. Moreover, we provide a certain condition for a compact quasi $k$-Yamabe soliton to be gradient, and for noncompact…
In this note we prove that a (anti-)self dual quasi Yamabe soliton with positive sectional curvature is rotationally symmetric. This generalizes a recent result of G. Huang and H. Li in dimension four. Whence, (anti-) self dual gradient…
In this paper, we completely classify nontrivial non-flat two- and three-dimensional complete gradient Yamabe solitons.
We consider the broadest concept of the gradient Yamabe soliton, the conformal gradient soliton. In this paper, we elucidate the structure of complete gradient conformal solitons under some assumption, and provide some applications to…
In this paper, we classify complete, nontrivial shrinking and steady quasi-Yamabe gradient solitons whose scalar curvature is bounded below by the soliton constant. We also classify complete, nontrivial expanding and steady quasi-Yamabe…
In this paper, we completely classify almost Yamabe solitons on hypersurfaces in Euclidean spaces arisen from the position vector field. Some results of almost Yamabe solitons with a concurrent vector field and almost Yamabe solitons on…
We study gradient Ricci solitons warped products whose base is the Euclidean space. We show that the warping functions of these manifolds are invariant under the (n-1)-dimensional translation group. We characterize the potential function…
A Yamabe soliton is defined on arbitrary almost contact B-metric manifold, which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The cases when…
By using the fiberwise spherical symmetrization we give a comparison theorem of Yamabe constants on warped products and prove the existence of radially-symmetric Yamabe minimizers on Riemannian manifolds given by products with round…
In this paper we consider $M = B\times_{f}F$ warped product gradient Ricci solitons. We proved that the potential function depends only on the base and the fiber $F$ is necessarily Einstein manifold. We provide all such solutions in the…
The goal of this article is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these…
In this paper, we show that any nontrivial complete shrinking gradient Yamabe soliton whose scalar curvature is bounded below by the soliton constant everywhere and is strictly greater than the constant at some point is rotationally…
We derive lower bounds on the scalar curvature of complete non-compact gradient Yamabe solitons under some integral curvature conditions. Based on this, we prove that the corresponding potential functions have at most quadratic growth in…
We provide the classification of locally conformally flat gradient Yamabe solitons with positive sectional curvature. We first show that locally conformally flat gradient Yamabe solitons with positive sectional curvature have to be…
We prove a necessary and sufficient condition for an asymptotically Euclidean manifold to be conformally related to one with specified nonpositive scalar curvature: the zero set of the desired scalar curvature must have a positive Yamabe…
In this paper, we show that any compact gradient k-Yamabe soliton must have constant $\sigma_k$-curvature. Moreover, we provide a certain condition for a compact k-Yamabe soliton to be gradient.
In this note, we prove triviality and nonexistence results for gradient Ricci soliton warped metrics. The proofs stem from the construction of gradient Ricci solitons that are realized as warped products, from which we know that the base…
We obtain existence results for a class of fully nonlinear Yamabe-type problems on non-compact manifolds, addressing both the so-called positive and negative cases. We also give explicit examples of manifolds with warped product ends and…