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 On almost $r$-paracontact Riemannian manifold with a certain connection Commun. Korean Math. Soc. 2010 Vol. 25, No. 2, 235-243 https://doi.org/10.4134/CKMS.2010.25.2.235Published online June 1, 2010 Mobin Ahmad, Abdul Haseeb, Jae-Bok Jun, and Shamsur Rahman Integral University, Integral University, Kook-Min University, and Integral University Abstract : In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter symmetric connections, even some of them are not introduced so far. So, in this paper, we define a quarter symmetric semi-metric connection in an almost $r$-paracontact Riemannian manifold and consider invariant, non-invariant and anti-invariant hypersurfaces of an almost $r$-paracontact Riemannian manifold with that connection. Keywords : almost $r$-paracontact Riemannian manifold, quarter-symmetric semi-metric connection MSC numbers : 53C05, 53D12 Downloads: Full-text PDF