Invariant Hypersurfaces Immersed in Almost Paracontact Riemannian Manifolds Ii

In thpvpaper4iin itpart If thpresent paper studed an invaiant hypersurface inersed in an almost paTacontact Rieian manifold with structure (1)5 and proved the following THEOREM A et nvutant hyper8urfae inenersed inn aZmost pavacontUet Riemannian mani oZd ntth Srer3n37L Then one Othe foZluing OSs ooeurs (1) isnornaZ o V Z this O8 ihTits an Z208 produt Rie-manni23tuatur exOpting Z 8)hei 2 indued aimo6tro240struOtztre tntSO is UliaZ () is g to this OS3 S ainost paraeontet Rtemanntan st17uue The main puIpose of this paper is to studyinvariant hypersurfaces iner sed in almost paracontact Rieian manifblds of 5evera1ecial k1ds In 111 give deftion of an alinost paracontact Riemannian1dd ast prcteianifold In 2 we shal1 disc uss general hyper-sfacesrsedast paracti-ifoldsha11 vestigate 3 anvariant h)esurfacemesed in an almost paractact Riennian manifolq with vanishing torsitesor In 4 and 5 we Shall study invariant hypersurface irsed in a paracontact Riemamianifold aPiifolddSiifold In 1ast 6shall c sider invariant hypersurfaces satisfing s(e conditions lhroughout this paper we assurne that manifolds and tensor fields consider are of class C