# $\mathcal{P}\mathcal{R}$-pseudo-slant warped product submanifold of a nearly paracosymplectic manifold

 Received: 31.III.2016, Accepted: 25.X.2016 Abstract. In this paper, we study $\mathcal{P}\mathcal{R}$-pseudo-slant warped product submanifold of a nearly paracosymplectic manifold $\widetilde{M}$. The necessary and sufficient condition is obtained for the distributions allied to the characterization of a $\mathcal{P}\mathcal{R}$-pseudo-slant submanifold being integrable and totally geodesic foliation. In addition, we have defined $\mathcal{P}\mathcal{R}$-pseudo-slant warped product submanifold of $\widetilde{M}$ and gave some illustrations. Finally, we extracted the constraints for a submanifold of $\widetilde{M}$ to be a $\mathcal{P}\mathcal{R}$-pseudo-slant warped product of the form $F\times_{f}N_{\lambda}$. Keywords: Warped product, Paracontact manifold, Pseudo-slant submanifold Mathematics Subject Classification (2010): 53B25, 53B30, 53C25, 53D15 Authors: S.K. Srivastava, Department of Mathematics, Central University of Himachal Pradesh, Dharamshala-176215, Himachal Pradesh, India A. Sharma, Department of Mathematics, Central University of Himachal Pradesh, Dharamshala-176215, Himachal Pradesh, India S.K. Tiwari, Department of Applied science, Ajay Kumar Garg Engg. College, Ghaziabad-201009, Uttar Pradesh, India