A Comprehensive Review of Solitonic Inequalities in Riemannian Geometry
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916352453771264 |
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| author | Chen, Bang-Yen Choudhary, Majid Ali Nisar, Mohammed Siddiqi, Mohd Danish |
| author_facet | Chen, Bang-Yen Choudhary, Majid Ali Nisar, Mohammed Siddiqi, Mohd Danish |
| contents | In 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Comprehensive Review of Solitonic Inequalities in Riemannian Geometry Chen, Bang-Yen Choudhary, Majid Ali Nisar, Mohammed Siddiqi, Mohd Danish Differential Geometry 53B25, 53C1, , 53C20, 53C21, 53C25, 53C40 In 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. |
| title | A Comprehensive Review of Solitonic Inequalities in Riemannian Geometry |
| topic | Differential Geometry 53B25, 53C1, , 53C20, 53C21, 53C25, 53C40 |
| url | https://arxiv.org/abs/2408.05312 |