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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (10): 56-63.doi: 10.6040/j.issn.1671-9352.0.2016.607

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具有半对称度量联络的广义Sasakian空间形式中的子流形的Chen-Ricci不等式

何国庆1,张量1,刘海蓉2   

  1. 1.安徽师范大学数学计算机科学学院, 安徽 芜湖 241003;2.南京林业大学理学院, 江苏 南京 210037
  • 收稿日期:2016-12-30 出版日期:2017-10-20 发布日期:2017-10-12
  • 作者简介:何国庆(1979— ), 女, 讲师, 研究方向为微分几何. E-mail: wh_hgq@126.com
  • 基金资助:
    安徽省自然科学基金资助项目(1408085MA01);安徽省高校自然科学基金资助项目(KJ2017A324);江苏省自然科学基金资助项目(BK20140965);南京林业大学高层次人才科研基金资助项目(G2014022)

Chen-Ricci inequalities for submanifolds of generalized Sasakian space forms with a semi-symmetric metric connection

HE Guo-qing1, ZHANG Liang1, LIU Hai-rong2   

  1. 1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China;
    2. School of Science, Nanjing Forestry University, Nanjing 210037, Jiangsu, China
  • Received:2016-12-30 Online:2017-10-20 Published:2017-10-12

摘要: 建立了具有半对称度量联络的广义Sasakian空间形式中关于子流形的Chen-Ricci不等式。 这些不等式刻画了子流形关于半对称度量联络的内在不变量(Ricci曲率)、k-Ricci曲率与外在不变量(平均曲率平方‖H‖2)之间的关系。

关键词: 半对称度量联络, 广义Sasakian空间形式, Chen-Ricci 不等式

Abstract: We establish Chen-Ricci inequalities for submanifolds of generalized Sasakian space forms endowed with a semi-symmetric metric connection. These inequalities give relationships between the squared mean curvature and certain intrinsic invariants involving the Ricci curvature and the k-Ricci curvature with respect to the induced semi-symmetric metric connection of submanifolds.

Key words: generalized Sasakian space forms, semi-symmetric metric connection, Chen-Ricci inequalities

中图分类号: 

  • O186.12
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[1] 刘旭东,潘旭林,张量. 具有半对称度量联络拟常曲率空间中子流形的Casorati曲率不等式[J]. 山东大学学报(理学版), 2017, 52(2): 55-59.
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