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Gap theorems for compact almost Ricci-harmonic solitons
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TLDR
The main focus of as mentioned in this paper is to establish necessary and sufficient conditions for almost Ricci-harmonic solitons and harmonic-Einstein metrics, which is a generalization of Ricci solITons.Abstract:
Almost Ricci-harmonic solitons are generalization of Ricci-harmonic solitons, almost Ricci solitons and harmonic-Einstein metrics. The main focus of this paper is to establish necessary and suffici...read more
Citations
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On the spectrum of the weighted p-Laplacian under the Ricci-harmonic flow
TL;DR: Abolarinwa et al. as discussed by the authors studied the spectrum of the weighted p-Laplacian on a complete Riemannian manifold evolving by the Ricci-harmonic flow and showed that the first eigenvalue diverges in a finite time along this flow.
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On the Entropy Formulas and Solitons for the Ricci-Harmonic Flow
TL;DR: In this paper, entropy monotonicity formulas and classification of gradient almost soliton for Ricci-harmonic flow were introduced and analyzed. But the authors did not consider the dynamical nature of the flow and treated the defining elliptic equations and relying on analytic techniques.
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Rigid properties of generalized $\tau$-quasi Ricci-harmonic metrics
TL;DR: In this paper, the authors studied the conditions under which generalized ε-quasi Ricci-harmonic metrics are harmonic-Einstein and gave some characterization results for it.
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Rigid Properties of Generalized $$\tau $$ τ -Quasi Ricci-Harmonic Metrics
TL;DR: In this paper, a special case of generalized Ricci-harmonic metrics is studied, called compact generalized �₷-RICCI-harmonics, and conditions under which these metrics are harmonic-Einstein.
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On sequential warped product manifolds admitting gradient Ricci-harmonic solitons
TL;DR: In this article , the main relations for a gradient Ricci-harmonic soliton on sequential warped product manifolds are given for both generalized Robertson-Walker space times and sequential standard static space-times.
References
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Three-manifolds with positive Ricci curvature
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Convergence of the Yamabe flow for arbitrary initial energy
TL;DR: In this article, the convergence of the Yamabe flow was shown to hold if the dimension of the initial metric is locally conformally flat and the curvature of the scalar curvature is known.
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Ricci almost solitons
TL;DR: The Ricci almost soliton as discussed by the authors is a natural extension of the concept of gradient Ricci soliton, and it has been shown to be a generalization of the Ricci Almost Soliton.
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Ricci almost solitons
TL;DR: The Ricci almost soliton as discussed by the authors is a natural extension of the concept of gradient Ricci soliton, and it can be seen as a natural solution to the problem of gradient almost solitons.