CERTAIN CURVATURE CONDITIONS ON KENMOTSU MANIFOLDS ADMITTING A QUARTER-SYMMETRIC METRIC CONNECTION

被引：1

作者：

Zhao, Peibiao ^{[1
]}

De, Uday Chand ^{[2
]}

Mandal, Krishanu ^{[2
]}

Han, Yanling ^{[3
]}

机构：

[1] Nanjing Univ Sci & Tecnol, Dept Appl Math, Nanjing, Jiangsu, Peoples R China

[2] Univ Calcutta, Dept Pure Math, Kol, W Bengal, India

[3] Qilu Univ Technol, Sch Sci, Jinan, Shandong, Peoples R China

来源：

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2018年 / 104卷 / 118期

基金：

中国国家自然科学基金;

关键词：

quarter-symmetric metric connection; Kenmotsu manifold; Ricci semisymmetric manifold; xi-concircularly flat manifold; xi-conformally flat manifold; xi-projectively flat manifold; Pseudo Ricci-symmetric manifold;

D O I：

10.2298/PIM1818169Z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study certain curvature properties of Kenmotsu manifolds with respect to the quarter-symmetric metric connection. First we consider Ricci semisymmetric Kenmotsu manifolds with respect to a quarter-symmetric metric connection. Next, we study xi-conformally flat and xi-concircularly flat Kenmotsu manifolds with respect to the quarter-symmetric metric connection. Moreover, we study Kenmotsu manifolds satisfying the condition (Z) over tilde (xi,Y) . (S) over tilde = 0, where (Z) over tilde and (S) over tilde are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Then, we prove the non-existence of xi-projectively flat and pseudo-Ricci symmetric Kenmotsu manifolds with respect to the quarter-symmetric metric connection. Finally, we construct an example of a 5-dimensional Kenmotsu manifold admitting a quarter-symmetric metric connection for illustration.

引用

页码：169 / 181

页数：13

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