Gap theorems for Ricci-harmonic solitons
Homare Tadano
TL;DR
This paper establishes gap theorems for Ricci-harmonic solitons using generalized Ricci curvature estimates, providing conditions under which these solitons are harmonic-Einstein, thus extending previous research in the field.
Contribution
It introduces new gap theorems for Ricci-harmonic solitons based on curvature estimates, generalizing prior results by Li and Fernandez-Lopez et al.
Findings
Necessary and sufficient conditions for Ricci-harmonic solitons to be harmonic-Einstein.
Extension of previous gap theorems to Ricci-harmonic solitons.
Use of generalized Ricci curvature estimates in proving theorems.
Abstract
In the present paper, by using estimates for the generalized Ricci curvature, we shall give some gap theorems for Ricci-harmonic solitons showing some necessary and sufficient conditions for the solitons to be harmonic-Einstein. Our results may be regarded as a generalization of recent works by H. Li, and M. Fernandez-Lopez and E. Garcia-Rio.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds