A Comprehensive Review of Solitonic Inequalities in Riemannian Geometry

Year 2024, , 727 - 752, 27.10.2024

Bang-yen Chen , Majid Ali Choudhary , Nisar Mohammed , Mohd Danish Siddiqi

https://doi.org/10.36890/iejg.1526047

Abstract

n Riemannian geometry, Ricci soliton inequalities are an important field of study that provide profound insights into the geometric and analytic characteristics of Riemannian manifolds. An extensive study of Ricci soliton inequalities is given in this review article, which also summarizes their historical evolution, core ideas, important findings, and applications. We investigate the complex interactions between curvature conditions and geometric inequalities as well as the several kinds of Ricci solitons, such as expanding, steady, and shrinking solitons. We also go over current developments, unresolved issues, and possible paths for further study in this fascinating area.

Keywords

Ricci soliton, solitonic inequalities, $D$-homothetic deformation, statistical submersion, hyperbolic Ricci soliton, Hitchin-Thorpe inequality

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