| 闭黎曼流形上临界度量的研究 |
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| 引用本文： | 肖飞,俞柏慧. 闭黎曼流形上临界度量的研究[J]. 井冈山大学学报(自然科学版), 2021, 42(4): 1-4 |
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| 作者姓名： | 肖飞 俞柏慧 |
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| 作者单位： | 井冈山大学数理学院,江西,吉安 343009 |
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| 基金项目： | 国家自然科学基金项目（11761032）；江西省自然科学基金重点项目（20202ACBL211001）；井冈山大学博士科研启动项目（JZB1921）. |
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| 摘 要： | 本文研究了闭黎曼流形上的双参数二次曲率泛函的临界度量,利用带Yamabe常数及曲率的pinching条件,以及我们证明了一个刚性定理.此外,我们也得到另外一些曲率条件下的刚性结果.
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| 关 键 词： | 二次曲率泛函 临界度量 Yamabe常数 |
| 收稿时间： | 2021-04-05 |
| 修稿时间： | 2021-05-26 |
CRITICAL POINTS FOR QUADRATIC CURVATURE FUNCTIONAL ON CLOSED MANIFOLDS |
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| XIAO Fei,YU Bai-hui. CRITICAL POINTS FOR QUADRATIC CURVATURE FUNCTIONAL ON CLOSED MANIFOLDS[J]. Journal of Jinggangshan University(Natural Sciences Edition), 2021, 42(4): 1-4 |
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| Authors: | XIAO Fei YU Bai-hui |
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| Affiliation: | School of Mathmatics Science& Physics, Jinggangshan University, Ji''an, Jiangxi 343009, China |
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| Abstract: | In this paper, the critical metrics for two-parameter quadratic curvature functionals on closed manifolds, and pinching conditions with Yamabe incariant and curvature were studied. Moreover, the results also provide a few rigidity results that involve the Weyl curvature, the trace-less Ricci curvature and the Yamabe invariant, accordingly. |
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| Keywords: | quadratic curvature functionals critical points Yamabe invariant |
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