A lower diameter bound for compact domain manifolds of shrinking Ricci-harmonic solitons

TL;DR

This paper establishes a lower bound on the diameter of compact manifolds that are shrinking Ricci-harmonic solitons, extending previous results in Ricci geometry to this more general setting.

Contribution

It provides the first lower diameter bound for compact shrinking Ricci-harmonic solitons, generalizing earlier bounds from Ricci soliton studies.

Findings

Derived a lower diameter bound for compact shrinking Ricci-harmonic solitons.

Extended previous Ricci soliton diameter bounds to Ricci-harmonic geometry.

Generalized known results to a broader class of geometric flows.

Abstract

In this paper, we shall give a lower diameter bound for compact domain manifolds of shrinking Ricci-harmonic solitons. Our result may be regarded as a generalization to Ricci-harmonic geometry of the recent works by Fern\'andez-L\'opez and Garc\'ia-R\'io (Q. J. Math. 61, 319--327, 2010), Futaki and Sano (Asian J. Math. 17, 17--32, 2013), and Futaki \textit{et al} (Ann. Global Anal. Geom. 44, 105--114, 2013).