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| The New Gap Theorem for Certain Riemannian Manifolds |
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Citation： |
Juan LI,Hongwei XU,Entao ZHAO.The New Gap Theorem for Certain Riemannian Manifolds[J].Chinese Annals of Mathematics B,2026,(1):251~270 |
| Page view： 211
Net amount： 107 |
Authors： |
Juan LI; Hongwei XU;Entao ZHAO |
Foundation： |
National Natural Science Foundation of China (Nos. 12471051, 12071424, 12171423) |
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| Abstract： |
In this paper, the authors investigate the geometric rigidity of Riemannian manifolds under suitable curvature restrictions. They prove a new gap theorem: if a locally conformally flat manifold of dimension n ≥ 5 has constant scalar curvature and its Ricci tensor is sufficiently close to that of a space form in Ln/2 norm, then the manifold is isometric to the space form. The proof uses the refined Kato inequality and analysis of the Cotton tensor. |
Keywords： |
Gap theorems Locally conformally flat manifolds Ricci curvature Constant scalar curvature Cotton tensor |
Classification： |
53C20, 53C25 |
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