| 摘要: |
| 本文研究了拟常曲率黎曼流形中子流形的Chen不等式.利用代数技巧,建立了Chen广义不等式、Chen-Ricci不等式和关于卷积函数和平均曲率平方的不等式,推广了Özgür和Chen的一些结果. |
| 关键词: Chen不等式 Chen-Ricci不等式 卷积 拟常曲率 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:Supported by the Foundation for Excellent Young Talents of Higher Education of Anhui Province (2011SQRL021ZD). |
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| SOME REMARKS ON GEOMETRIC INEQUALITIES FOR SUBMANIFOLDS OF A RIEMANNIAN MANIFOLD OF QUASI-CONSTANT CURVATURE |
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ZHANG Pan, ZHANG Liang, SONG Wei-dong
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School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China
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| Abstract: |
| In this paper, we study Chen's inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature. By using algebraic techniques, we establish Chen's general inequalities, Chen-Ricci inequalities and inequalities between the warping function and the squared mean curvature, which generalize several rusults of Özgür and Chen's. |
| Key words: Chen's inequalities Chen-Ricci inequalities warped product quasi-constant curvature |
