We prove that a nontrivial complete generalized quasi Yamabe gradient soliton (M; g) must be a quasi Yamabe gradient soliton on each connected component of M and that a nontrivial complete locally conformally at generalized quasi Yamabe gradient soliton has a special warped product structure.
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14 results for “quasi-Yamabe”
The study characterizes quasi Yamabe solitons with potential vector fields.
problem Characterizing quasi Yamabe solitons with specific properties.
method Analyzing potential vector fields and their norms in quasi Yamabe solitons.
result If the potential vector field has a finite global norm in a complete non-trivial, non-compact quasi Yamabe soliton with finite volume, the scalar curvature becomes constant and the soliton reduces to a Yamabe soliton.
We consider almost quasi-Yamabe solitons in Riemannian manifolds, derive a Bochner-type formula in the gradient case and prove that under certain assumptions, the manifold is of constant scalar curvature. We also provide necessary and sufficient conditions for a gradient almost quasi-Yamabe soliton on the base manifold…
The study classifies specific types of solitons with bounded scalar curvature.
problem Classifying quasi-Yamabe gradient solitons with bounded scalar curvature.
method Analyzing complete, nontrivial solitons with scalar curvature bounded above or below.
result Classification of specific types of solitons with bounded scalar curvature.
In this paper, we introduce the concept of quasi Yamabe gradient solitons, which generalizes the concept of Yamabe gradient solitons. By using some ideas in [7,8], we prove that -dimensional complete quasi Yamabe gradient solitons with vanishing Weyl curvature tensor and positive sectional curvature must …
The paper characterizes a class of almost Kenmotsu manifolds with quasi Yamabe solitons.
problem Characterizing almost Kenmotsu manifolds with quasi Yamabe solitons.
method Analyzing the properties of quasi Yamabe solitons on -almost Kenmotsu manifolds.
result If a -almost Kenmotsu manifold admits a quasi Yamabe soliton, then is a constant multiple of , is a strict infinitesimal contact transformation, and for any vector field .
The study of quasi Yamabe solitons on 3D contact metric manifolds with specific curvature condition.
problem Investigating quasi Yamabe solitons on 3D contact metric manifolds with a specific curvature condition.
method Analyzing the properties of quasi Yamabe solitons on 3D contact metric manifolds with Qφ = φQ and proving the conditions under which the soliton vector field is constant, the scalar curvature is constant, and the manifold is Sasakian.
result If a 3D contact metric manifold M with Qφ = φQ admits a quasi Yamabe soliton with a non-zero soliton vector field V collinear with the Reeb vector field ξ, then V is a constant multiple of ξ, the scalar curvature is constant, and the manifold is Sasakian.
In this paper we initiate the study of Yamabe and quasi-Yamabe solitons on Euclidean submanifolds whose soliton fields are the tangential components of their position vector fields. Several fundamental results of such solitons were proved. In particular, we classify such Yamabe and quasi-Yamabe solitons on Euclidean hy…
Study on gradient solitons on specific manifolds.
problem Existence and properties of gradient solitons on warped product manifolds.
method Analyzing necessary and sufficient conditions for the existence of generalized quasi Yamabe gradient solitons.
result Existence of non-trivial gradient Yamabe solitons on specific spacetimes.
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 Yamabe solitons with positive sectional curvature is rotationally symmetric. We als…
This paper classifies Kähler manifolds with specific Einstein-type properties.
problem Classifying gradient Einstein-type Kähler manifolds with .
method Unified framework of Einstein-type manifolds, focusing on classification with .
result Complete classification of non-trivial, complete gradient Einstein-type Kähler manifolds with .
The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In fact, its statistical counterpart, that is, Kenmotsu statistical manifold also has same importance as that of Kenmotsu manifold. Theoretical physicists have also b…
This paper classifies solitons under specific tensor conditions.
problem Classifying solitons under vanishing conditions on the Weyl, Cotton, and Cao-Chen tensors.
method Analyzing complete conformal gradient solitons and using tensor conditions.
result Classification of complete nontrivial locally conformally flat conformal gradient solitons.
Study on -Ricci-Yamabe solitons on Riemannian submersions.
problem Characterizing -Ricci-Yamabe solitons on Riemannian submersions.
method Analyzing conditions for -Ricci-Yamabe solitons on submersions and deriving Laplacian equations.
result Classification of fiber and target manifolds as -Ricci-Yamabe solitons under various conditions.