@article{Mofarreh2022, 
author = {Fatemah Mofarreh and S. K. Srivastava and Anuj Kumar and Akram Ali},
title = {Geometric inequalities of        P    R  -warped product submanifold in para-Kenmotsu manifold},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {10},
pages = {19481-19509},
keywords = {para contact manifold, submanifold, warped product},
url = {https://www.sciopen.com/article/10.3934/math.20221069},
doi = {10.3934/math.20221069},
abstract = {The main purpose of this paper is to study the properties of        P    R  -semi-invariant submanifold of para-Kenmotsu manifold. We obtain the integrability conditions for the invariant distribution and anti-invariant distribution. We obtain some existence and non-existence results of        P    R  -semi-invariant warped product submanifolds. We provide some necessary and sufficient conditions for        P    R  -semi-invariant submanifold to be a        P    R  -semi-invariant warped product submanifold in para-Kenmotsu manifold. We also derive some sharp inequalities for        P    R  -semi-invariant warped product submanifold in para-Kenmotsu manifolds.}
}