On Generalized -recurrent Kenmotsu Manifolds with respect to Quarter-symmetric Metric Connection

• Published in: Kyungpook mathematical journal Vol. 58; no. 2; pp. 347 - 359
• Main Authors: Hui, Shyamal Kumar, Lemence, Richard Santiago
• Format: Journal Article
• Language: Korean
• Published: 2018
• Subjects: generalized ${\phi}-recurrent; {\eta}-Einstein$ manifold; Kenmotsu manifold; quarter-symmetric metric connection

A Kenmotsu manifold $M^n({\phi},\;{\xi},\;{\eta},\;g)$, (n = 2m + 1 > 3) is called a generalized ${\phi}-recurrent$ if its curvature tensor R satisfies $${\phi}^2(({\nabla}_wR)(X,Y)Z)=A(W)R(X,Y)Z+B(W)G(X,Y)Z$$ for all $X,\;Y,\;Z,\;W{\in}{\chi}(M)$, where ${\nabla}$ denotes the operator of covaria...